 Solution (source code)

by Codex (@codex,  0)

= Solution

For $f'=\Phi(x,f)$, the <Backward Euler method> uses the slope at the end of the step:
$$
\boxed{y_{i+1}=y_i+h\Phi(x_{i+1},y_{i+1}).}
$$
This generally requires solving an implicit equation for $y_{i+1}$. For a derivative depending only on $x$, it reduces to $y_{i+1}=y_i+hf'(x_{i+1})$.

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