Differential Equations MCQs with Answers 2027

Q21

With K as a constant, the solution possible for the first order differential equation

\frac{dy}{dx} = e^{- 3 x}

is

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Q22

Open question

The solution of the first order differential equation x'(t) = -3x(t), x(0) = x₀ is

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Q23

Open question

The solution of the equation

x \frac{dy}{dx} + y = 0

passing through the point (1, 1) is

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Q24

Open question

With initial condition x(1) = 0.5, the solution of the differential equation,

t \frac{dx}{dt} + x = t

is

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Q25

Open question

For the differential equation

\frac{d ^{2} x}{d t ^{2}} + 6 \frac{dx}{dt} + 8 x = 0

with initial conditions x(0) = 1 and

\frac{dx}{dy}_{t = 0} = 0,

the solution is

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Q26

Open question

Transformation to linear form by substituting v = y^{1 - n} of the equation

\frac{dy}{dt} + p (t) y = q (t) y^{n}; n > 0

will be

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Q27

Open question

Consider the differential equation

y ¨ + 2 y ˙ + y = 0

with boundary conditions y(0) = 1, y(1) = 0. The value of y(2) is

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Q28

Open question

For the equation,

\frac{dy}{dx} + 7 x^{2} y = 0,

if

y (0) = \frac{3}{7},

then the value of y(1) is

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Q29

Open question

Consider two solutions x(t) = x₁(t) and x(t) = x₂(t) of the differential equation

\frac{d ^{2} x ( t )}{d t ^{2}} + x (t) = 0, t > 0,

such that

x_{2} = 0, \frac{d x _{2} ( t )}{dt}_{t = 0} = 1.

The Wronskian

{\text{W}}\left( {\text{t}} \right) = \left| {\begin{array}{*{20}{c}} {{{\text{x}}_1}\left( {\text{t}} \right)}&{{{\text{x}}_2}\left( {\text{t}} \right)} \\ {\frac{{{\text{d}}{{\text{x}}_1}\left( {\text{t}} \right)}}{{{\text{dt}}}}}&{\frac{{{\text{d}}{{\text{x}}_2}\left( {\text{t}} \right)}}{{{\text{dt}}}}} \end{array}} \right|

at

t = \frac{π}{2}

is

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Q30

Open question

If

\frac{d ^{2} y}{d t ^{2}} + y = 0

under the conditions y = 1,

\frac{dy}{dt} = 0,

when t = 0, then y is equal to

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Q31

Open question

The general solution of

\frac{d ^{2} y}{d x ^{2}} + y = 0

is

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Q32

Open question

The solution for the differential equation

\frac{dy}{dx} = x^{2} y

with the condition that y = 1 at x = 0 is

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Q33

Open question

The solution of the differential equation

\frac{dy}{dx} = ky, y (0) = c

is

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Q34

Open question

The solution of the differential equation

\frac{dy}{dx} + y^{2} = 0

is

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Q35

Open question

If y = 2x³ - 3x² + 3x - 10, the value of ∆³y will be (where, ∆ is forward differences operator)

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Q36

Open question

Match List-I with List-II and select the correct answer:

List-I	List-II
A. $\frac{dy}{dx} = \frac{y}{x}$	1. Circles
B. $\frac{dy}{dx} = - \frac{y}{x}$	2. Straight lines
C. $\frac{dy}{dx} = \frac{x}{y}$	3. Hyperbolas
D. $\frac{dy}{dx} = - \frac{x}{y}$

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Q37

Open question

If a and b are constants, the most general solution of the differential equation

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{dx}{dt} + x = 0

is

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Q38

Open question

The solution of the differential equation, for t > 0, y''(t) + 2y'(t) + y(t) = 0 with initial conditions y(0) = 0 and y'(0) = 1, is (u(t) denotes the unit step function),

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Q39

Open question

A differential equation is given as

x^{2} \frac{d ^{2} y}{d x ^{2}} - 2 x \frac{dy}{dx} + 2 y = 4

The solution of differential equation in terms of arbitrary constant C₁ and C₂ is

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Q40

Open question

The solution of the differential equation

\frac{d ^{2} y}{d x ^{2}} = 0

with boundary conditions

i . \frac{dy}{dx} = 1 at x = 0; ii . \frac{dy}{dx} = 1 at x = 1 is

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Differential Equationspractice.

Differential Equations
practice.