Question Bank • QB_EM_ADV_054
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 for the first-order linear differential equation $\frac{dy}{dx} + y \cot(x) = 2 \cos(x)$ on the interval $(0, \pi)$ is:
Options:
-
(A) $\sin(x)$
-
(B) $\cos(x)$
-
(C) $\ln|\sin(x)|$
-
(D) $\csc(x)$
Step-by-Step Solution & Explanation
Here $P(x) = \cot(x)$. The integrating factor is:
$\text{I.F.} = e^{\int P(x) \, dx} = e^{\int \cot(x) \, dx} = e^{\ln|\sin(x)|} = \sin(x)$
for $x \in (0, \pi)$.
Practice In Authentic CBT Exam Interface
Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.
Launch CBT Mock Test