Allied & ICAR Exam Bank • ALLIED_0069 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

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

Question Statement:

Given $\frac{dy}{dx} = -2y$ with $y(0) = 5$, the value of $y(0.5)$ (rounded off to two decimal places) is:

Answer Key:

1.84

Step-by-Step Solution & Explanation

$y(x) = 5 e^{-2x}$. At $x = 0.5$, $y(0.5) = 5 e^{-1} = \frac{5}{2.71828} \approx 1.8394 \approx 1.84$.
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