 Solution

ID: past-exam-of-the-numerical-analysis-course-of-the-university-of-oxford/2021/3/b/i/solution

For

f (x, y) = - x y^{2}

, the explicit Euler method evaluates the right-hand side at the known point

(x_{n}, y_{n})

. Therefore

y_{n + 1} = y_{n} - h x_{n} y_{n}^{2} = y_{n} (1 - h x_{n} y_{n}), y_{0} = 1.

This update requires no root finding.

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