Suppose that we use Euler's method to approximate the solution to the differential equation:
dy/dx=x¹y; y(0.2)=7.
Let f(x,y)=x¹/y.
We let x0=0.2 and y0=7 and pick a step size h=0.2. Euler's method is the following algorithm. From xₙ and yₙ, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing

xₙ₊₁ = xₙ + h, yₙ₊₁ = yₙ + h⋅f(xₙ, yₙ )

Complete the following table:

n xₙ yₙ
0 0.4 1
1 0.6 1.08
2 0.8 1.22814
3 1
4 1.2
5 1.4

1) The exact solution can also be found using the separation of variables.
It is y(x)=?
2) Thus the actual value of the function at point x = 1.4.
y(1.4)=?