Allied & ICAR Exam Bank • ALLIED_2702 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Homogeneous differential equations

Question Statement:

The solution to $\frac{dy}{dx} + y = 0$ with $y(0) = 5$ at $x = 2$ is $5 e^k$. The value of $k$ is:

Answer Key:

-2

Step-by-Step Solution & Explanation

$y(x) = 5 e^{-x}$. At $x = 2$, $y(2) = 5 e^{-2}$. Hence $k = -2$.
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