GATE & PSUs - Engineering Mathematics & General Aptitude (Common)

Partial Differential Equations (Heat, Wave & Laplace Equations) question bank (Differential Equations)

Practice 8 free GATE & PSUs - Engineering Mathematics & General Aptitude (Common) Differential Equations - Partial Differential Equations (Heat, Wave & Laplace Equations) questions with answers and step-by-step solutions.

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Q1.

[Partial Differential Equations (Heat, Wave & Laplace Equations) Concept 4] What is the general solution of the second-order ordinary differential equation $\frac{d^2 y}{dx^2} + 4\frac{dy}{dx} + 4y = 0$?

(A)

$y(x) = (C_1 + C_2 x) e^{-2x}$

(B)

$y(x) = C_1 e^{-2x} + C_2 e^{2x}$

(C)

$y(x) = C_1 \cos(2x) + C_2 \sin(2x)$

(D)

$y(x) = C_1 e^{-4x} + C_2$

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Q2.

[Partial Differential Equations (Heat, Wave & Laplace Equations) Concept 8] What is the general solution of the second-order ordinary differential equation $\frac{d^2 y}{dx^2} + 4\frac{dy}{dx} + 4y = 0$?

(A)

$y(x) = (C_1 + C_2 x) e^{-2x}$

(B)

$y(x) = C_1 e^{-2x} + C_2 e^{2x}$

(C)

$y(x) = C_1 \cos(2x) + C_2 \sin(2x)$

(D)

$y(x) = C_1 e^{-4x} + C_2$

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