Allied & ICAR Exam Bank • ALLIED_0786 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

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

Question Statement:

For the initial value problem $\frac{dy}{dx} + 3y = 0$ with $y(0) = 5$, the value of $y(t)$ at $t = \frac{\ln 5}{3}$ is:

Answer Key:

1.0

Step-by-Step Solution & Explanation

$y(t) = 5 e^{-3t}$. For $t = \frac{\ln 5}{3}$, $y = 5 e^{-\ln 5} = 5 \times \frac{1}{5} = 1.0$.
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