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For the first order initial value problem: \frac{d y}{d x}=x y^{2}, \quad y(0)=5 use the Euler iteration method i.e. y_{n+1}=y_{n}+h f_{n} to calculate the values yn+1, for n = 0,1,2

using a step size h = 0.1. By separating variables solve the equation exactly and hence compute the errors in the Euler approximation for the three iteration steps (writing your answers to 6 decimal places).

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