Differential Equations MCQs with Answers 2027

Q61

The general solution of the differential equation

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{dy}{dx} - 5 y = 0

in terms of arbitrary constants K₁ and K₂ is

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Q62

Open question

General solution of the Cauchy-Euler equation

x^{2} \frac{d ^{2} y}{d x ^{2}} - 7 x \frac{dy}{dx} + 16 y = 0

is

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Q63

Open question

Biotransformation of an organic compound having concentration (x) can be modeled using an ordinary differential equation

\frac{dx}{dt} + k x^{2} = 0,

where k is the reaction rate constant. If x = a at t = 0, the solution of the equation is

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Q64

Open question

The solution of initial value problem;

\frac{\partial u}{\partial x} = 2 \frac{\partial u}{\partial t} + u,

where u(x, 0) = 6e^-3x is

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Q65

Open question

A function n(x) satisfies the differential equation

\frac{d ^{2} n ( x )}{d x ^{2}} - \frac{n ( x )}{L ^{2}} = 0

where L is a constant. The boundary conditions are: n(0) = K and n(

\infty

) = 0. The solution to this equation is

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Q66

Open question

The solutions of differential equation

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

are

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Q67

Open question

It is given that y'' + 2y' + y = 0, y(0) = 0, y(1) = 0. What is y (0.5)?

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Q68

Open question

A function y(t), such that y(0) = 1 and y(1) = 3e^-1, is a solution of the differential equation

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

Then y(2) is

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Q69

Open question

A curve passes through the point (x = 1, y = 0) and satisfies the differential equation

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

The equation that describes the curve is

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Q70

Open question

The differential equation

\frac{dy}{dx} + 4 y = 5

is valid in the domain 0 ≤ x ≤ 1 with y(0) = 2.25. The solution of differential equation is

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Q71

Open question

The degree of the differential equation

\frac{d ^{2} x}{d t ^{2}} + 2 x^{3} = 0

is

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Q72

Open question

The solution for the differential equation

\frac{d ^{2} x}{d t ^{2}} = - 9 x

with initial conditions x(0) = 1 and

\frac{dx}{dt}_{t = 0} = 1,

is

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Q73

Open question

Consider the differential equation:

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

The general solution with constant c is

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Q74

Open question

A spherical naphthalene ball exposed to the atmosphere loses volume at a rate proportional to its instantaneous surface area due to evaporation. If the initial diameter of the ball is 2 cm and the diameter reduces to 1 cm after 3 months, the ball completely evaporates in

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Q75

Open question

The particular solution of the initial value problem given below is