JEE Exam  >  JEE Notes  >  Mathematics (Maths) Class 12  >  NCERT Solutions - Exercise 9.2: Differential Equations

NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations

Q1: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Ans: 
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Differentiating both sides of this equation with respect to x, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Now, differentiating equation (1) with respect to x, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Substituting the values ofNCERT Solutions Class 12 Maths Chapter 9 - Differential Equationsin the given differential equation, we get the L.H.S. as:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Thus, the given function is the solution of the corresponding differential equation.

Q2: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Ans: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Differentiating both sides of this equation with respect to x, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Substituting the value ofNCERT Solutions Class 12 Maths Chapter 9 - Differential Equationsin the given differential equation, we get:
L.H.S. =NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations= R.H.S.
Hence, the given function is the solution of the corresponding differential equation.

Q3: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Ans: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Differentiating both sides of this equation with respect to x, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Substituting the value ofNCERT Solutions Class 12 Maths Chapter 9 - Differential Equationsin the given differential equation, we get:
L.H.S. =NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations= R.H.S.
Hence, the given function is the solution of the corresponding differential equation.

Q4: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Ans: 
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Differentiating both sides of the equation with respect to x, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
NCERT Solutions Class 12 Maths Chapter 9 - Differential EquationsL.H.S. = R.H.S.
Hence, the given function is the solution of the corresponding differential equation.

Q5: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Ans: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Differentiating both sides with respect to x, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Substituting the value ofNCERT Solutions Class 12 Maths Chapter 9 - Differential Equationsin the given differential equation, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Hence, the given function is the solution of the corresponding differential equation.

Q6: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Ans: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Differentiating both sides of this equation with respect to x, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Substituting the value ofNCERT Solutions Class 12 Maths Chapter 9 - Differential Equationsin the given differential equation, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Hence, the given function is the solution of the corresponding differential equation.

Q7: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Ans: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Differentiating both sides of this equation with respect to x, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations L.H.S. = R.H.S.
Hence, the given function is the solution of the corresponding differential equation.

Q8: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Ans: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Differentiating both sides of the equation with respect to x, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Substituting the value ofNCERT Solutions Class 12 Maths Chapter 9 - Differential Equationsin equation (1), we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Hence, the given function is the solution of the corresponding differential equation.

Q9: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Ans: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Differentiating both sides of this equation with respect to x, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Substituting the value ofNCERT Solutions Class 12 Maths Chapter 9 - Differential Equationsin the given differential equation, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Hence, the given function is the solution of the corresponding differential equation.

Q10: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Ans: NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Differentiating both sides of this equation with respect to x, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Substituting the value ofNCERT Solutions Class 12 Maths Chapter 9 - Differential Equationsin the given differential equation, we get:
NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations
Hence, the given function is the solution of the corresponding differential equation.

Q11: 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
Ans: 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.

Q12: 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
Ans: In a particular solution of a differential equation, there are no arbitrary constants.
Hence, the correct answer is D.

The document NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations is a part of the JEE Course Mathematics (Maths) Class 12.
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FAQs on NCERT Solutions Class 12 Maths Chapter 9 - Differential Equations

1. What is a differential equation?
Ans. A differential equation is an equation that involves one or more derivatives of an unknown function. It relates the rate of change of the function with its value at different points.
2. What is the order of a differential equation?
Ans. The order of a differential equation is the highest order of the derivative present in the equation. For example, a differential equation with a second derivative is a second-order differential equation.
3. How are differential equations classified?
Ans. Differential equations can be classified as ordinary differential equations (ODEs) or partial differential equations (PDEs) based on whether the unknown function depends on one variable or multiple variables, respectively.
4. What is the general solution of a differential equation?
Ans. The general solution of a differential equation is a solution that contains all possible solutions of the equation. It includes arbitrary constants that can be determined by applying initial conditions or boundary conditions.
5. How are differential equations used in real-world applications?
Ans. Differential equations are used in various fields such as physics, engineering, biology, economics, and more to model and analyze phenomena that involve rates of change. They help in predicting the behavior of systems over time.
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