Allied & ICAR Exam Bank • ALLIED_0785 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

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

Question Statement:

The solution to the separable ODE $\frac{dy}{dx} = \frac{x}{y}$ with initial condition $y(0) = 2$ is:

Options:

  • (A) $y^2 - x^2 = 4$
  • (B) $y^2 + x^2 = 4$
  • (C) $y = 2 e^x$
  • (D) $y = x + 2$

Answer Key:

A

Step-by-Step Solution & Explanation

Separating variables: $y dy = x dx \implies \frac{y^2}{2} = \frac{x^2}{2} + C \implies y^2 - x^2 = 2C$. At $(0, 2)$, $4 - 0 = 2C \implies 2C = 4 \implies y^2 - x^2 = 4$.
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