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' = -5x⁴y², y(0) = 1, h = 0.2, Sol. y = 1/(1 + x)⁵