Allied & ICAR Exam Bank • ALLIED_2707 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Higher order linear ODEs with constant coefficients

Question Statement:

A particular integral of $\frac{d^2 y}{dx^2} - 4y = e^{3x}$ is:

Options:

  • (A) $\frac{1}{5} e^{3x}$
  • (B) $\frac{1}{9} e^{3x}$
  • (C) $\frac{1}{13} e^{3x}$
  • (D) $e^{3x}$

Answer Key:

A

Step-by-Step Solution & Explanation

$y_p = \frac{1}{D^2 - 4} e^{3x} = \frac{1}{3^2 - 4} e^{3x} = \frac{1}{5} e^{3x}$.
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