Allied & ICAR Exam Bank • ALLIED_2700 NAT • 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 $\frac{dy}{dx} + \frac{3}{x} y = x^2$ for $x > 0$ is $x^k$. The integer $k$ is:

Answer Key:

3

Step-by-Step Solution & Explanation

$I(x) = e^{\int (3/x) dx} = e^{3 \ln x} = x^3$. Hence $k = 3$.
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