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Differential Equations - 8 - Mathematics MCQ


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20 Questions MCQ Test Topic-wise Tests & Solved Examples for Mathematics - Differential Equations - 8

Differential Equations - 8 for Mathematics 2024 is part of Topic-wise Tests & Solved Examples for Mathematics preparation. The Differential Equations - 8 questions and answers have been prepared according to the Mathematics exam syllabus.The Differential Equations - 8 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Differential Equations - 8 below.
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Differential Equations - 8 - Question 1

General solution of equation (sin x - x cos x)y" - (x sin x) y' + (sin x)y = 0, given that y = sin x is a solution

Differential Equations - 8 - Question 2

If M(x, y)dx + N(x, y)dy = 0 and  then

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Differential Equations - 8 - Question 3

The equation  is linear differential equation of first order, if

Differential Equations - 8 - Question 4

An integrating factor of x dy/dx + (3x + 1)y = xe–2x is

Detailed Solution for Differential Equations - 8 - Question 4


which is a linear differential equation

 

Differential Equations - 8 - Question 5

What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)2 + 1 = 0? 

Detailed Solution for Differential Equations - 8 - Question 5

Given: (y’)2 + 1 = 0 Consider if y = 2x, then y’ = 2 and hence the left-hand side of the equation becomes 3 which is greater than 1. Therefore, the left-hand side of the equation will always be greater than, or equal to one and thus cannot be zero and hence the differential equation is not satisfied.

Differential Equations - 8 - Question 6

What is the order of the partial differential equation,

Detailed Solution for Differential Equations - 8 - Question 6

The order of an equation is defined as the highest derivative present in the equation. Hence, in the given equation, the order is 2.

Differential Equations - 8 - Question 7

A particular integral of y" - (a + b)y' + aby = Q(x) is, 

Differential Equations - 8 - Question 8

The homogeneous differential equation M(x, y)dx, N(x, y) dy = 0 can be reduced to a differential equation, In which the variable are separated, by the substitution 

Differential Equations - 8 - Question 9

General solution of  

Differential Equations - 8 - Question 10

 is the general solution of

Differential Equations - 8 - Question 11

In linear ordinary differential equation, the dependent variable and its differential coefficients are not multiplied together and occurs only in

Differential Equations - 8 - Question 12

General solution of the equation   Given that y = sin x is a solution, is

Differential Equations - 8 - Question 13

Solve d3y/dx3 - d2y/dx2 - 4dy/dx + 4y = 0 has the solution

Detailed Solution for Differential Equations - 8 - Question 13

Given equation is (D3 – D2 – 4D + 4)y = 0 

A.E. is m3 – m2 – 4m + 4 = 0  m2(m – 1) – 4(m – 1) = 0 

(m – 1) (m2 – 4) = 0 

m = 1, m = ± 2 

m1 = 1, m2 = 2, m3 = – 2

∴ The general solution of the given equation is y = C1ex + C2 e2x + C3 e-2x 

Differential Equations - 8 - Question 14

The P.I. of the differential equation (D3 - D)y = ex + e-x is

Differential Equations - 8 - Question 15

If φ(x, y) = 0 is a singular solution, then φ(x, y) is a factor of

Differential Equations - 8 - Question 16

P.I . of 

Differential Equations - 8 - Question 17

The complementaiy function of (D4 - a4)y = 0 is

Differential Equations - 8 - Question 18

A differential equation of first order and first degree is homogeneous, if

Differential Equations - 8 - Question 19

The integrating factor for the differential equation 

Differential Equations - 8 - Question 20

Given, an equation  and a solution of it is y = a0 + a1 sinh x + a2 cosh x, where a0, a1, a2 are arbitrary constants, then this solution is

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