Allied & ICAR Exam Bank • ALLIED_0104 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical solutions of ODEs

Question Statement:

Using Euler's explicit method to solve $\frac{dy}{dx} = 2x$ with $y(0) = 1$ and step size $h = 0.5$, the value of $y(0.5)$ is:

Answer Key:

1

Step-by-Step Solution & Explanation

$y_{n+1} = y_n + h f(x_n, y_n) = 1 + 0.5(2 \times 0) = 1.0$.
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