Given that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} - 2{y^2} = {{\text{e}}^x}\) and y = 1 when x = 0, use Euler’s method with a step length of 0.1 to find an approximation for the value of y when x = 0.4. Give all intermediate values with maximum possible accuracy.

\(\frac{{{\text{d}}y}}{{{\text{d}}x}} = {{\text{e}}^x} + 2{y^2}\)     (A1)

required approximation = 3.85     A1

[8 marks]

Most candidates seemed familiar with Euler’s method. The most common way of losing marks was either to round intermediate answers to insufficient accuracy despite the advice in the question or simply to make an arithmetic error. Many candidates were given an accuracy penalty for not rounding their answer to three significant figures.