Allied & ICAR Exam Bank • ALLIED_2701 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

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

Question Statement:

Bernoulli's differential equation $\frac{dy}{dx} + P(x) y = Q(x) y^n$ with $n \neq 0, 1$ is transformed into a linear ODE by substituting:

Options:

  • (A) $v = y^{1-n}$
  • (B) $v = y^{n-1}$
  • (C) $v = y^n$
  • (D) $v = \ln y$

Answer Key:

A

Step-by-Step Solution & Explanation

Dividing by $y^n$ gives $y^{-n} y' + P y^{1-n} = Q$. Setting $v = y^{1-n} \implies v' = (1-n) y^{-n} y'$ transforms it into linear ODE $\frac{dv}{dx} + (1-n) P v = (1-n) Q$.
← Previous (ALLIED_2700) Next (ALLIED_2702) →

Practice In Authentic CBT Exam Interface

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

Launch CBT Mock Test