Allied & ICAR Exam Bank • ALLIED_1003 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: First order equations

Question Statement:

The integrating factor for the first-order linear differential equation $\frac{dy}{dx} + \left(\frac{2x}{1 + x^2}\right)y = \frac{1}{(1+x^2)^2}$ is:

Options:

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

Answer Key:

A

Step-by-Step Solution & Explanation

Integrating factor $I.F. = e^{\int P(x) dx} = e^{\int \frac{2x}{1+x^2} dx} = e^{\ln(1+x^2)} = 1+x^2$.
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