Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability / 6 / d / ii / Solution

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