# Suppose that we use Euler's method to approximate the solution to the differential equation

ππ¦/ππ₯=π₯^4/π¦ π¦(0.1)=1

Let π(π₯,π¦)=π₯^4/π¦.

We let π₯0=0.1 and π¦0=1 and pick a step size β=0.2. Euler's method is the the following algorithm. From π₯π and π¦π, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing