NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Mathematics (Maths) Class 12

JEE : NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The document NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
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Differential Equations

Question 1: Determine order and degree(if defined) of differential equation NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : -

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The highest order derivative present in the differential equation isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. Therefore, its order is four.

The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.

 

Question 2: Determine order and degree(if defined) of differential equation NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - The given differential equation is:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The highest order derivative present in the differential equation isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. Therefore, its order is one.

It is a polynomial equation inNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. The highest power raised toNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevis 1. Hence, its degree is one.

 

Question 3: Determine order and degree(if defined) of differential equation NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : -

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The highest order derivative present in the given differential equation isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. Therefore, its order is two.

It is a polynomial equation inNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevandNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. The power raised toNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevis 1.

Hence, its degree is one.

Question 4: Determine order and degree(if defined) of differential equation NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : -

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The highest order derivative present in the given differential equation isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. Therefore, its order is 2.

The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.

Question 5: Determine order and degree(if defined) of differential equation NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : -

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The highest order derivative present in the differential equation isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. Therefore, its order is two.

It is a polynomial equation inNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevand the power raised toNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevis 1.

Hence, its degree is one.

 

Question 6: Determine order and degree(if defined) of differential equation NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The highest order derivative present in the differential equation isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. Therefore, its order is three.

The given differential equation is a polynomial equation inNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev.

The highest power raised toNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevis 2. Hence, its degree is 2.

Question 7: Determine order and degree(if defined) of differential equation NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The highest order derivative present in the differential equation isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. Therefore, its order is three.

It is a polynomial equation inNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. The highest power raised toNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevis 1. Hence, its degree is 1.

 

Question 8: Determine order and degree(if defined) of differential equation NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : -

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The highest order derivative present in the differential equation isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. Therefore, its order is one.

The given differential equation is a polynomial equation inNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevand the highest power raised toNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevis one. Hence, its degree is one.

 

Question 9: Determine order and degree(if defined) of differential equation NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The highest order derivative present in the differential equation isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. Therefore, its order is two.

The given differential equation is a polynomial equation inNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevandNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevand the highest power raised toNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevis one.

Hence, its degree is one.

 

 Question 10: Determine order and degree(if defined) of differential equation NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The highest order derivative present in the differential equation isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. Therefore, its order is two.

This is a polynomial equation inNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevandNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevand the highest power raised toNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevis one. Hence, its degree is one.

 

Question 11: The degree of the differential equation NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevis

(A) 3  

(B) 2   

 (C) 1        

 (D) not defined

 

ANSWER : -

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The given differential equation is not a polynomial equation in its derivatives. Therefore, its degree is not defined.

Hence, the correct answer is D.

 

Question 12: The order of the differential equationNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevis

(A) 2                           

(B) 1                                       

(C) 0                           

(D) not defined

 

ANSWER : -

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

The highest order derivative present in the given differential equation isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev. Therefore, its order is two.

Hence, the correct answer is A.

 

Question 13: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : -

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides of this equation with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Now, differentiating equation (1) with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting the values ofNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevin the given differential equation, we get the L.H.S. as:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Thus, the given function is the solution of the corresponding differential equation.

 

 Question 14: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides of this equation with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting the value ofNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevin the given differential equation, we get:

L.H.S. =NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev= R.H.S.

Hence, the given function is the solution of the corresponding differential equation.

 

Question 15: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides of this equation with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting the value ofNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevin the given differential equation, we get:

L.H.S. =NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev= R.H.S.

Hence, the given function is the solution of the corresponding differential equation.

 

Question 16: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : -

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides of the equation with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevL.H.S. = R.H.S.

Hence, the given function is the solution of the corresponding differential equation.

 

Question 17: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting the value ofNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevin the given differential equation, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Hence, the given function is the solution of the corresponding differential equation.

 

Question 18: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides of this equation with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting the value ofNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevin the given differential equation, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Hence, the given function is the solution of the corresponding differential equation.

 

 Question 19: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides of this equation with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev L.H.S. = R.H.S.

Hence, the given function is the solution of the corresponding differential equation.

 

Question 20: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides of the equation with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting the value ofNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevin equation (1), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Hence, the given function is the solution of the corresponding differential equation.

 

Question 21: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides of this equation with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting the value ofNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevin the given differential equation, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Hence, the given function is the solution of the corresponding differential equation.

 

Question 21: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides of this equation with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting the value ofNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevin the given differential equation, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Hence, the given function is the solution of the corresponding differential equation.

 

Question 22: The numbers of arbitrary constants in the general solution of a differential equation of fourth order are:

(A) 0                           

(B) 2                                       

(C) 3                                      

(D) 4

 

ANSWER : - We know that the number of constants in the general solution of a differential equation of order n is equal to its order.

Therefore, the number of constants in the general equation of fourth order differential equation is four.

Hence, the correct answer is D. 

 

Question 23: The numbers of arbitrary constants in the particular solution of a differential equation of third order are:

(A) 3                           

(B) 2                                       

(C) 1                                       

(D) 0

 

ANSWER : - In a particular solution of a differential equation, there are no arbitrary constants.

Hence, the correct answer is D.

 

Question 24: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides of the given equation with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Again, differentiating both sides with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Hence, the required differential equation of the given curve isNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

 

Question 25: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Again, differentiating both sides with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Dividing equation (2) by equation (1), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required differential equation of the given curve.

 

Question 26: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides with respect to x, we get: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Again, differentiating both sides with respect to x, we get: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Multiplying equation (1) with (2) and then adding it to equation (2), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Now, multiplying equation (1) with 3 and subtracting equation (2) from it, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting the values of NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevin equation (3), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required differential equation of the given curve.

 

Question 27: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Multiplying equation (1) with equation (2) and then subtracting it from equation (2), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides with respect to x, we get: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Dividing equation (4) by equation (3), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required differential equation of the given curve.

 

Question 28: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Again, differentiating with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Adding equations (1) and (3), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required differential equation of the given curve.

 

Question 29: Form the differential equation of the family of circles touching the y-axis at the origin.

ANSWER : - The centre of the circle touching the y-axis at origin lies on the x-axis.

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Let (a, 0) be the centre of the circle.

Since it touches the y-axis at origin, its radius is a.

Now, the equation of the circle with centre (a, 0) and radius (a) is

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating equation (1) with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Now, on substituting the value of a in equation (1), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required differential equation.

 

Question 30: Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - The equation of the parabola having the vertex at origin and the axis along the positive y-axis is:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating equation (1) with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Dividing equation (2) by equation (1), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required differential equation.

 

Question 31: Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.

ANSWER : - The equation of the family of ellipses having foci on the y-axis and the centre at origin is as follows:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating equation (1) with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Again, differentiating with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting this value in equation (2), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required differential equation.

 

Question 32: Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin.

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

 

ANSWER : - The equation of the family of hyperbolas with the centre at origin and foci along the x-axis is:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating both sides of equation (1) with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Again, differentiating both sides with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting the value ofNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevin equation (2), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required differential equation.

 

Question 33: Form the differential equation of the family of circles having centre on y-axis and radius 3 units.

ANSWER : - Let the centre of the circle on y-axis be (0, b).

The differential equation of the family of circles with centre at (0, b) and radius 3 is as follows:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating equation (1) with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting the value of (y – b) in equation (1), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required differential equation.

 

Question 34: Which of the following differential equations hasNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevas the general solution?

A. NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev                                              

B. NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

C. NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev                                    

D. NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

 

ANSWER : - The given equation is:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Differentiating with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Again, differentiating with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required differential equation of the given equation of curve.

Hence, the correct answer is B.

 

Question 35: Which of the following differential equation hasNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRevas one of its particular solution?

A. NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev                                            

 B. NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

C. NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev                                          

  D. NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

 

ANSWER : - The given equation of curve is yx.

Differentiating with respect to x, we get: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Again, differentiating with respect to x, we get: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Now, on substituting the values of yNCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev from equation (1) and (2) in each of the given alternatives, we find that only the differential equation given in alternative Cis correct.

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Hence, the correct answer is C.

 

 

 Question 36: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - The given differential equation is:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Now, integrating both sides of this equation, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required general solution of the given differential equation.

 

 Question 37: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - The given differential equation is:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Now, integrating both sides of this equation, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required general solution of the given differential equation.

 

 Question 38: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - The given differential equation is:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Now, integrating both sides, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required general solution of the given differential equation.

 

 Question 39: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - The given differential equation is:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Integrating both sides of this equation, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting these values in equation (1), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required general solution of the given differential equation.

Question 40: NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

ANSWER : - The given differential equation is:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Integrating both sides of this equation, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Let (ex   e–x) = t.

Differentiating both sides with respect to x, we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

Substituting this value in equation (1), we get:

NCERT Solutions (Part - 1) - Differential Equations JEE Notes | EduRev

This is the required general solution of the given differential equation.

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