Use Eulers method to approximate the solution to the followi

Use Euler\'s method to approximate the solution to the following intial value problem at the points x = 1.1, 1.2, and 1.3 using steps of size 0.1. Use 3 decimal places.

y\'= x + y² ,   y(0) = 1

Solution

f(x,y)=x+y^2

h=0.1

y0=1,x0=0

y_{n+1}=y_n+hf(x_n,y_n)=y_n+0.1*(x_n+y_n^2)

We solve this in excel sheet

We get the following table

Hence,