Question Bank • QB_EM_166 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical solutions of ODEs

Question Statement:

Using Euler's explicit method with step size $h = 0.1$, solve $\frac{dy}{dx} = x + y$ with initial condition $y(0) = 1$. Calculate the value of $y(0.1)$.

Answer Key:

1.1

Step-by-Step Solution & Explanation

Euler's update formula: $y_{n+1} = y_n + h f(x_n, y_n)$ Given $x_0 = 0, y_0 = 1, h = 0.1$: $f(x_0, y_0) = 0 + 1 = 1$ $y_1 = 1 + (0.1)(1) = 1.1$
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