GATE AG 2010 • Q1 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Linear and non-linear first order Ordinary Differential Equations (ODE)

Question Statement:

A particular solution of $\frac{d^2y}{dx^2} + 5\frac{dy}{dx} - 3y = 6$ is:

Options:

  • (A) 2.0
  • (B) 0.5
  • (C) -0.5
  • (D) -2.0

Official Answer Key:

D

Step-by-Step Solution & Explanation

For a constant forcing term, try a constant particular solution y = c. Then y′ = y″ = 0, so the ODE reduces to −3c = 6, giving c = −2.0. Options (A)/(B)/(C) come from sign or arithmetic slips (e.g. dividing 6 by 3 without the negative sign, or by −5).

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