Question Bank • QB_SUB_EM_0126 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

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

Question Statement:

The integrating factor for the first-order linear differential equation $\frac{dy}{dx} + P(x) y = Q(x)$ is given by:

Options:

  • (A) $e^{\int P(x)\, dx}$
  • (B) $e^{-\int Q(x)\, dx}$
  • (C) $\int P(x)\, dx$
  • (D) $P(x) Q(x)$

Answer Key:

A

Step-by-Step Solution & Explanation

Multiplying by $I.F. = e^{\int P(x)\, dx}$ makes the left-hand side the exact derivative $\frac{d}{dx}[y \cdot I.F.]$.
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