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

Euler-Cauchy Equations & Method of Variation of Parameters question bank (Differential Equations)

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Q1.

[Euler-Cauchy Equations & Method of Variation of Parameters Concept 3] 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.

[Euler-Cauchy Equations & Method of Variation of Parameters Concept 7] 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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