Question Bank • QB_EM_DE_001 MCQ • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

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

Question Statement:

The integrating factor for the linear first-order differential equation $\frac{dy}{dx} + \frac{2}{x}y = x^3$ for $x > 0$ is:

Options:

  • (A) $x^2$
  • (B) $2\ln(x)$
  • (C) $e^{2x}$
  • (D) $\frac{1}{x^2}$

Answer Key:

A

Step-by-Step Solution & Explanation

This is a first-order linear ODE of standard form $\frac{dy}{dx} + P(x)y = Q(x)$ where $P(x) = \frac{2}{x}$. The integrating factor $IF$ is: $IF = e^{\int P(x) dx} = e^{\int \frac{2}{x} dx} = e^{2 \ln(x)} = e^{\ln(x^2)} = x^2$ Thus, option A is correct.
← Previous (QB_EM_ADV_055) Next (QB_EM_108) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test