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Differential Equations - 3 - Mathematics MCQ


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20 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Differential Equations - 3

Differential Equations - 3 for Mathematics 2024 is part of Topic-wise Tests & Solved Examples for Mathematics preparation. The Differential Equations - 3 questions and answers have been prepared according to the Mathematics exam syllabus.The Differential Equations - 3 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Differential Equations - 3 below.
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Differential Equations - 3 - Question 1

Solving by variation of parameter y" - 2y'+ y = exlog x, the value of wronskion W is

Detailed Solution for Differential Equations - 3 - Question 1

Correct Answer :- d

Explanation : We have (D2 – 2D + 1)y = ex logx 

A.E. is m2 – 2m + 1 = 0 

i.e., (m – 1)2 = 0 

i.e., m = 1, 1  

Hence C.F. is  yc = (C1 + C2x)ex 

= C1ex + C2xex  

∴ y = Aex + Bxex ...(1) 

We have  y1 = ex and y2 = xex

y′1 = ex, y′2 = xex + ex 

W = y1y'2 - y2y'1 

= xe2x + e2x – xe2x

= e2x

Differential Equations - 3 - Question 2

The general solution of the equation 

Detailed Solution for Differential Equations - 3 - Question 2

Given, differential equation is

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Differential Equations - 3 - Question 3

The c-discriminant of the equations 
(y - c)2 = x(x - a)2 is

Detailed Solution for Differential Equations - 3 - Question 3

Given, differential equation is
(y - c)2 = x(x - a)2

Differential Equations - 3 - Question 4

If y1(x) and y2(x) are solutions of y" + x2y' + (1 - x)y = 0 such that

then the Wronskian W( y1, y2) on R is

Detailed Solution for Differential Equations - 3 - Question 4

We have

Differential Equations - 3 - Question 5

If yand yare two solutions of initial value problem y" + p(x)y' + q(x)y = 0, y(x0) = y0, y'(x0) = y0 and the Wronskion W(y1, y2) = 0, then yand y2 are

Differential Equations - 3 - Question 6

Which of the following transformation reduce the differential equation   into the form 

Differential Equations - 3 - Question 7

The general solution for  is

Detailed Solution for Differential Equations - 3 - Question 7

Differential Equations - 3 - Question 8

  in the domain R : |x| < 5, |y| < 3 the equation has

Differential Equations - 3 - Question 9

For IVP
y’ = 2y1/2, y(0) = 0
Which one is correct in a nbd of 0?

Differential Equations - 3 - Question 10

Detailed Solution for Differential Equations - 3 - Question 10

Differential Equations - 3 - Question 11

If e-x, xe-x are solutions of y" + ay' + by = 0, then

Differential Equations - 3 - Question 12

The degree of differential equation satisfying the relation 

Differential Equations - 3 - Question 13

The process of formation of the differential equation is given in the wrong order, select the correct option from below given options. 
1) Eliminate the arbitrary constants. 
2) Differential equation which involves x, y, dy / dx
3) Differentiating the given equation w.r.t x as many times as the number of arbitrary constants. 

Detailed Solution for Differential Equations - 3 - Question 13

The correct order of forming differential equation is given by option 3, 1, 2, even the given differential equation can be solved by other order given in the option but the task becomes more tedious.

Differential Equations - 3 - Question 14

The singular solution of the differential equation p3 + px - y = 0 is

Differential Equations - 3 - Question 15

Which of the following relations hold true? 

Detailed Solution for Differential Equations - 3 - Question 15

The properties of vector or cross product, for the orthogonal vectors, i, j, and k are, 
i × i = j × j = k × k = 0, 
i × j = k, j × i = -k, 
j × k = i, k × j = -i, 
k × i = j, i × k = -j

Differential Equations - 3 - Question 16

Solving by variation of parameter for the equation y" + y = sec x, the value of Wronskion is

Differential Equations - 3 - Question 17

The eigen values for the boundary value problem x" + λx = 0; x(0) = 0, x(π) + x'(π) = 0 satisfy

Differential Equations - 3 - Question 18

Suppose yp(x) = x cos 2(x) is a particular solution of y" + αy = - 4 sin (2x)
Then, the constant α equals

Differential Equations - 3 - Question 19

All real solutions of the differential equation y" + 2ay' + by = cos x (where a and b are real constants) are periodic if

Differential Equations - 3 - Question 20

Integrating factor of (x7y2 + 3y)dx + (3x8y - x)dy = 0 is xmyn, then

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