Question Bank • QB_EM_121 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Homogeneous differential equations

Question Statement:

The differential equation $\frac{dy}{dx} = \frac{x^2 + y^2}{2xy}$ can be transformed into a separable ODE by substituting:

Options:

  • (A) $y = v x$
  • (B) $y = v + x$
  • (C) $y = v x^2$
  • (D) $y = \frac{v}{x}$

Answer Key:

A

Step-by-Step Solution & Explanation

The numerator $x^2 + y^2$ and denominator $2xy$ are both homogeneous functions of degree 2. Hence, substituting $y = v x$ (where $\frac{dy}{dx} = v + x \frac{dv}{dx}$) reduces the ODE to variables separable in $v$ and $x$.
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