Allied & ICAR Exam Bank • ALLIED_0067 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Higher order linear ODEs with constant coefficients

Question Statement:

The general solution of $\frac{d^2 y}{dx^2} + 9y = 0$ is $y = C_1 \cos(k x) + C_2 \sin(k x)$. The value of $k$ is:

Answer Key:

3

Step-by-Step Solution & Explanation

Characteristic equation $m^2 + 9 = 0 \implies m = \pm 3i$. The roots are purely imaginary with frequency $k = 3$.
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