Allied & ICAR Exam Bank • ALLIED_0065 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 $\frac{dy}{dx} + \frac{2}{x} y = x^3$ for $x > 0$ is:

Options:

  • (A) $x^2$
  • (B) $\ln(x^2)$
  • (C) $e^{2x}$
  • (D) $x$

Answer Key:

A

Step-by-Step Solution & Explanation

$\text{I.F.} = e^{\int (2/x) dx} = e^{2\ln x} = x^2$.
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