This is the simplest method to explain numerically solving an ODE, more precisely, an initial value problem (IVP). Using the method, to get a feel for numerics as well as for the nature of IVPs, solve the IVP numerically with a PC or a calculator, 10 steps. Graph the computed values and the solution curve on the same coordinate axes.
y' = (y - x)²
y(0) = 0
h = 0.1
Sol. y = x - tanh x