Allied & ICAR Exam Bank • ALLIED_2776 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical solutions of ODEs

Question Statement:

Using Euler's method with $h = 0.2$ to solve $\frac{dy}{dx} = 2x$ with $y(0) = 0$, the value of $y(0.4)$ after two steps is:

Answer Key:

0.08

Step-by-Step Solution & Explanation

Step 1: $y(0.2) = y(0) + 0.2(2 \times 0) = 0$. Step 2: $y(0.4) = y(0.2) + 0.2(2 \times 0.2) = 0 + 0.2(0.4) = 0.08$.
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