Allied & ICAR Exam Bank • ALLIED_2697 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 ODE $\frac{dy}{dx} + P(x) y = Q(x)$ is:

Options:

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

Answer Key:

A

Step-by-Step Solution & Explanation

Multiplying by $I(x) = e^{\int P(x) dx}$ transforms the left side into $\frac{d}{dx}[y \cdot I(x)]$.
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