Question Bank • QB_EM_ADV_059 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Higher order linear ODEs with constant coefficients

Question Statement:

The particular integral $y_p$ of the ordinary differential equation $\frac{d^2y}{dx^2} + 9y = e^{2x}$ is:

Options:

  • (A) $\frac{1}{13} e^{2x}$
  • (B) $\frac{1}{5} e^{2x}$
  • (C) $\frac{1}{9} e^{2x}$
  • (D) $\frac{1}{4} e^{2x}$

Answer Key:

A

Step-by-Step Solution & Explanation

Using the inverse differential operator method: $y_p = \frac{1}{D^2 + 9} e^{2x}$ Since $D^2 + 9$ evaluated at $D = 2$ is $2^2 + 9 = 13 \neq 0$: $y_p = \frac{1}{2^2 + 9} e^{2x} = \frac{1}{13} e^{2x}$
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