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This mock test of Differential Equations - 8 for Mathematics helps you for every Mathematics entrance exam.
This contains 20 Multiple Choice Questions for Mathematics Differential Equations - 8 (mcq) to study with solutions a complete question bank.
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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

Solution:

QUESTION: 2

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

Solution:

QUESTION: 3

The equation is linear differential equation of first order, if

Solution:

QUESTION: 4

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

Solution:

which is a linear differential equation

QUESTION: 5

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

Solution:

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.

QUESTION: 6

What is the order of the partial differential equation,

Solution:

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

QUESTION: 7

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

Solution:

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

Solution:

QUESTION: 9

General solution of

Solution:

QUESTION: 10

is the general solution of

Solution:

QUESTION: 11

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

Solution:

QUESTION: 12

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

Solution:

QUESTION: 13

Solve d^{3}y/dx^{3} - d^{2}y/dx^{2} - 4dy/dx + 4y = 0 has the solution

Solution:

Given equation is (D^{3} – D^{2} – 4D + 4)y = 0

A.E. is m^{3} – m^{2} – 4m + 4 = 0 m^{2}(m – 1) – 4(m – 1) = 0

(m – 1) (m^{2} – 4) = 0

m = 1, m = ± 2

m_{1} = 1, m_{2} = 2, m_{3} = – 2

∴ The general solution of the given equation is y = C_{1}e^{x} + C_{2} e^{2x} + C_{3} e^{-2x}

QUESTION: 14

The P.I. of the differential equation (D^{3} - D)y = e^{x} + e^{-x}, is

Solution:

QUESTION: 15

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

Solution:

QUESTION: 16

P.I . of

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QUESTION: 17

The complementaiy function of (D^{4} - a^{4})y = 0 is

Solution:

QUESTION: 18

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

Solution:

QUESTION: 19

The integrating factor for the differential equation

Solution:

QUESTION: 20

Given, an equation and a solution of it is y = a_{0} + a_{1} sinh x + a_{2} cosh x, where a_{0}, a_{1}, a_{2} are arbitrary constants, then this solution is

Solution:

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- Differential Equations - 8
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- Differential Equations - 18
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- Differential Equations - 13
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- Differential Equations - 14
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- Differential Equations - 16
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