Allied & ICAR Exam Bank • ALLIED_0075 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Higher order linear ODEs with constant coefficients

Question Statement:

The particular integral of $\frac{d^2 y}{dx^2} + y = e^{2x}$ is $\frac{1}{k} e^{2x}$. The value of $k$ is:

Answer Key:

5

Step-by-Step Solution & Explanation

$y_p = \frac{1}{D^2 + 1} e^{2x} = \frac{1}{2^2 + 1} e^{2x} = \frac{1}{5} e^{2x} \implies k = 5$.
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