Allied & ICAR Exam Bank • ALLIED_0079 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

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

Question Statement:

The solution to $\frac{dy}{dx} = 3x^2$ with $y(0) = 4$ at $x = 2$ is:

Answer Key:

12

Step-by-Step Solution & Explanation

$y = x^3 + C$. At $x = 0, y = 4 \implies C = 4$. $y(x) = x^3 + 4$. At $x = 2$, $y(2) = 2^3 + 4 = 12$.
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