Differential Equations MCQs with Answers 2027

Q1

The general solution of the differential equation,

\frac{d ^{4} y}{d x ^{4}} - 2 \frac{d ^{3} y}{d x ^{3}} + 2 \frac{d ^{2} y}{d x ^{2}} - 2 \frac{dy}{dx} + y = 0

is

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Q2

Open question

The solution of the differential equation,

y 1 - x^{2} dy + x 1 - y^{2} dx = 0

is

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Q3

Open question

The maximum value of the solution y(t) of the differential equation

y (t) + y ¨ (t) = 0

with initial conditions

y ˙ (0) = 1

and y(0) = 1, for t ≥ 0 is

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Q4

Open question

The order of the differential equation

\frac{d ^{2} y}{d t ^{2}} + (\frac{dy}{dt})^{3} + y^{4} = e^{- t}

is

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Q5

Open question

The order and degree of the differential equation

\frac{d ^{3} y}{d x ^{3}} + 4 (\frac{dy}{dx})^{3} + y^{2} = 0

are respectively

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Q6

Open question

Consider the following second-order differential equation: y" - 4y' + 3y = 2t - 3t²
The particular solution of the differential equation is

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Q7

Open question

The differential equation

[1 + (\frac{dy}{dx})^{2}]^{3} = C^{2} [\frac{d ^{2} y}{d x ^{2}}]^{2}

is of

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Q8

Open question

Consider a system governed by the following equations:

\frac{d x _{1} ( t )}{dt} = x_{2} (t) - x_{1} (t); \frac{d x _{2} ( t )}{dt} = x_{1} (t) - x_{2} (t)

The initial conditions are such that

x_{1} (0) < x_{2} (0) < \infty.

Let

x_{1 f} = t \to \infty lim x_{1} (t)

and

x_{2 f} = t \to \infty lim x_{2} (t) .

Which one of the following is true?

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Q9

Open question

The families of curves represented by the solution of the equation

\frac{dy}{dx} = - (\frac{x}{y})^{n}

for n = -1 and n = +1, respectively, are

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Q10

Open question

The solution of

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

with initial value y(0) = 1 bounded in the interval

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Q11

Open question

The respective expressions for complimentary function and particular integral part of the solution of the differential equation

\frac{d ^{4} y}{d x ^{4}} + 3 \frac{d ^{2} y}{d x ^{2}} = 108 x^{2}

are

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Q12

Open question

The solution of the differential equation

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

with y(0) = y'(0) = 1 is

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Q13

Open question

Consider the differential equation

(t^{2} - 81) \frac{dy}{dt} + 5 ty = sin (t)

with y(1) = 2π. There exists a unique solution for this differential equation when t belongs to the interval

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Q14

Open question

The solution to 6yy' - 25x = 0 represents a

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Q15

Open question

Which one of the following is the general solution of the first order differential equation

\frac{dy}{dx} = (x + y - 1)^{2},

where x, y are real?

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Q16

Open question

If roots of the auxiliary equation of

\frac{d ^{2} y}{d x ^{2}} + a \frac{dy}{dx} + by = 0

are real and equal, the general solution of the differential equation is

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Q17

Open question

The solution of the ordinary differential equation

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

for the boundary condition, y = 5 at x = 1 is

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Q18

Open question

If y is the solution of the differential equation

y^{3} \frac{dy}{dx} + x^{3} = 0, y (0) = 1

the value of y(-1) is

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Q19

Open question

The general solution of the differential equation

\frac{dy}{dx} = cos (x + y),

with c as a constant, is

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Q20

Open question

The solution of the differential equation,

\frac{d ^{2} y}{d x ^{2}} - \frac{dy}{dx} - 2 y = 3 e^{2 x},

where, y(0) = 0 and y'(0) = -2 is

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Differential Equationspractice.

Differential Equations
practice.