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This mock test of Differential Equations - 14 for Mathematics helps you for every Mathematics entrance exam.
This contains 20 Multiple Choice Questions for Mathematics Differential Equations - 14 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The boundary value problem x ∈ [0, π], y(0), = 0, y(π) = 0 has

Solution:

QUESTION: 2

A lineal- differential equation

Solution:

QUESTION: 3

A differenlial equation dy/dx = y tanx - 2sin x has an integrating factor

Solution:

QUESTION: 4

Equation

Solution:

m^{2} - 3m + 2 = 0

⇒ m = 1, 2

QUESTION: 5

The general solution of the differential equation

Solution:

QUESTION: 6

The solution of the differential equation where C is a constant.

Solution:

QUESTION: 7

The degree of the differential equation

Solution:

QUESTION: 8

The integrating factor of the differential equation is calculated as

Solution:

QUESTION: 9

The solution of the recurrence relation x_{n} = 2 (x_{n-1} + x_{n-2}) with x_{1} = 1 and x_{2} = 1 - √3 is

Solution:

QUESTION: 10

Which of the following transformations reduces the given differential equation into homogeneous one?

Solution:

If x = X + h and y = Y + k is taken, then h - k + 1 = 0 and h + 2k - 3 = 0

QUESTION: 11

The solution of the differential equation y'' + 4y = 0 subject to y(0) = 1, y’ (0) = 2 is

Solution:

QUESTION: 12

General solution of the differential equation x dy = (y+ xe^{-y/x})dx is given by

Solution:

So differential equation (1) is

QUESTION: 13

A particular solution of the differential equation (D^{4} + 2D^{2} - 3) y = e^{x} is

Solution:

QUESTION: 14

A particular solution of the differentia! equation y"'- 3y'' + 3y' - y = e^{x} cos 2x is

Solution:

y''' + 3y" - y = e^{x} cos 2x .....(i)

It’s particular integral is

QUESTION: 15

If y = In (sin (x + a)) + b, where a and b are constants, is the primitive, then the corresponding lowest order differential equation is

Solution:

QUESTION: 16

Solution of the differential equation xy' + sin 2y = x^{3} sin^{2}y is

Solution:

which is a linear differential equation, so,

QUESTION: 17

The general solution of the differential equation y"' + y" - y' - y = 0 is

Solution:

QUESTION: 18

The solution of the differential equation

Solution:

For the given differential equation

M = x^{2}y+ xy^{2}

so the differential equation is exact so, its solution is

QUESTION: 19

Let y[x) = x sin x be one of the solution of an n^{th} order linear differential equation with constant coefficients. Then the minimum value of n is

Solution:

x sin x is one of the solution then x cos x, sin x, cos x must be the part of the solution, so minimum order of diffeerenlial equation will be 4.

QUESTION: 20

The solution of the initial value problem xy’ - y = 0 with y(1) = 1 is

Solution:

In y = In x + In c

y = cx

Al x = 1; y = 1, so eq. (1) becomes

1 = C. 1 ⇒ C= 1

so y(x) = x.

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