GATE AG 2012 • Q13 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 of the differential equation $(x + 1)\frac{dy}{dx} - y = \sin x$ is:

Options:

  • (A) x
  • (B) (x + 1)
  • (C) 1/x
  • (D) 1/(x + 1)

Official Answer Key:

D

Step-by-Step Solution & Explanation

Rewrite in standard linear form: dy/dx - y/(x+1) = sin x /(x+1), so P(x) = -1/(x+1). Integrating factor I.F. = e^∫P dx = e^(-∫dx/(x+1)) = e^(-ln(x+1)) = 1/(x+1). Answer: D.

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test