Allied & ICAR Exam Bank • ALLIED_0080 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 $\frac{dy}{dx} + P(x) y = Q(x) y^n$ is converted into a linear differential equation by substituting:

Options:

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

Answer Key:

A

Step-by-Step Solution & Explanation

Dividing by $y^n$: $y^{-n} y' + P y^{1-n} = Q$. Setting $v = y^{1-n} \implies v' = (1-n) y^{-n} y'$, transforming it to linear form.
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