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Differential Equations - 7 - Mathematics MCQ


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20 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Differential Equations - 7

Differential Equations - 7 for Mathematics 2024 is part of Topic-wise Tests & Solved Examples for Mathematics preparation. The Differential Equations - 7 questions and answers have been prepared according to the Mathematics exam syllabus.The Differential Equations - 7 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Differential Equations - 7 below.
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Differential Equations - 7 - Question 1

A particular solution of the differential equation 

Detailed Solution for Differential Equations - 7 - Question 1



Differential Equations - 7 - Question 2

Let y (x) = x sin x be one of the solution of an nth order linear differential equation with constant coefficients.
Then the minimum value of n is

Detailed Solution for Differential Equations - 7 - Question 2


 ...(i)

 ...(ii)
(i) + (ii) implies 

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Differential Equations - 7 - Question 3

The general solution of the differential equation

Detailed Solution for Differential Equations - 7 - Question 3


So, solution is 
So, 

and 

= ex (-sin x + 2 cos x)

Differential Equations - 7 - Question 4

The general solution of the differential equation y"(x) - 4y'(x) + 8y(x) = 10ex cos x is

Differential Equations - 7 - Question 5

The general solution of the differential equation ( x + y - 3) dx - (2x + 2y + 1) dy = 0 is

Detailed Solution for Differential Equations - 7 - Question 5


Let V = x + y
Then 
implies 
or 
implies 
implies 

Differential Equations - 7 - Question 6

If y(x) satisfies  with y(0) = 0, then  y(x) equals

Detailed Solution for Differential Equations - 7 - Question 6

Here IF = e2x
So, solution is

implies 
Hence, 

Differential Equations - 7 - Question 7

The solution of the differential equation yy' + y2 - x = 0, where c is a constant, is

Detailed Solution for Differential Equations - 7 - Question 7


The differential equation becomes

So, I.F. = e2x
and solution is

implies 
implies 
Equation of Circles of centered at (1,0) is given by 
 (x - 1)2 + y2 = λ2
.Where λ is parameter
Differentialing w.r.t. x, we get 
2(x - 1) + 2yy' = 0 
So, differential equation is

Differential Equations - 7 - Question 8

The differential equation representing all circles centred at (1, 0) is

Differential Equations - 7 - Question 9

General solution of 

Detailed Solution for Differential Equations - 7 - Question 9

We have 
Hence, solution is

implies 
implies 

Differential Equations - 7 - Question 10

 has the solution 

Detailed Solution for Differential Equations - 7 - Question 10


or m = -2, m = 1
Hence, General solution is y = 

Differential Equations - 7 - Question 11

The differential equation y" + 6y' + 9y = 50 e2x have particular integral

Detailed Solution for Differential Equations - 7 - Question 11

We have

Differential Equations - 7 - Question 12

The particular solution of

Detailed Solution for Differential Equations - 7 - Question 12


Differential Equations - 7 - Question 13

The c-discriminant and p-discriminant both contain

Detailed Solution for Differential Equations - 7 - Question 13

The p-discriminant equated to zero may include the envelope (E) once, the cusp-locus (C) once and tac-locus (T) twice implies ECT2

Differential Equations - 7 - Question 14

The c-discriminant does not contain one of the following,

Differential Equations - 7 - Question 15

Let φ1( (x) and φ2(x) are particular integral of L(y) = eax - f (x), a, b being constants, then a PI of L(y) = 2 beax is

Differential Equations - 7 - Question 16

Solution of the differential equation (a2 - 2xy - y2) dx = (x +y)2 dy is

Differential Equations - 7 - Question 17

The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point (4, 3). The equation of the curve is

Detailed Solution for Differential Equations - 7 - Question 17

We have,
Slope = dy/dx ⇒ dy/dx = 1/2y ⇒ 2 y dy = dx
Integrating both sides, we get y2 = x + C This passes through (4, 3)
∴ 9 = 4 + C ⇒ C = 5
So, the equation of the curve is y2 = x + 5

Differential Equations - 7 - Question 18

Order and degree of the differential equation  are respectively

Differential Equations - 7 - Question 19

Find the general solution of:

Detailed Solution for Differential Equations - 7 - Question 19

Rearranging we get;

dy/√(4 – y2) = dx

Integrating both the sides, we get;

∫dy/√(4 – y2) = ∫dx

We know that, by the formula;

∫1/√(a2 – x2) = sin-1(x/a)

Therefore,

sin-1y/2 = x+c

Differential Equations - 7 - Question 20

The solution of the differential equation  is

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