Question Bank • QB_EM_151 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

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

Question Statement:

For the first-order linear ordinary differential equation $\frac{dy}{dx} + \frac{2}{x} y = x^3$ ($x > 0$), the integrating factor $I(x)$ is:

Options:

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

Answer Key:

A

Step-by-Step Solution & Explanation

The integrating factor is: $I(x) = e^{\int P(x)\, dx} = e^{\int \frac{2}{x}\, dx} = e^{2 \ln x} = e^{\ln(x^2)} = x^2$
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