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Mathematics Exam  >  Mathematics Tests  >  Topic-wise Tests & Solved Examples for Mathematics  >  Differential Equations - 7 - Mathematics MCQ

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.
Solutions of Differential Equations - 7 questions in English are available as part of our Topic-wise Tests & Solved Examples for Mathematics for Mathematics & Differential Equations - 7 solutions in Hindi for Topic-wise Tests & Solved Examples for Mathematics course. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free. Attempt Differential Equations - 7 | 20 questions in 60 minutes | Mock test for Mathematics preparation | Free important questions MCQ to study Topic-wise Tests & Solved Examples for Mathematics for Mathematics Exam | Download free PDF with solutions
Differential Equations - 7 - Question 1
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A particular solution of the differential equation 

Detailed Solution for Differential Equations - 7 - Question 1



Differential Equations - 7 - Question 2
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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
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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
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The general solution of the differential equation y"(x) - 4y'(x) + 8y(x) = 10ex cos x is
Differential Equations - 7 - Question 5
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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
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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
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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
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The differential equation representing all circles centred at (1, 0) is
Differential Equations - 7 - Question 9
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General solution of 
Detailed Solution for Differential Equations - 7 - Question 9

We have 
Hence, solution is

implies 
implies 

Differential Equations - 7 - Question 10
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 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
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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
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The particular solution of
Detailed Solution for Differential Equations - 7 - Question 12


Differential Equations - 7 - Question 13
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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
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The c-discriminant does not contain one of the following,
Differential Equations - 7 - Question 15
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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
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Solution of the differential equation (a2 - 2xy - y2) dx = (x +y)2 dy is
Differential Equations - 7 - Question 17
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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
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Order and degree of the differential equation  are respectively
Differential Equations - 7 - Question 19
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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
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The solution of the differential equation  is
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