1Using Eulers method find an approximation to the solution o

1.Using Euler\'s method, find an approximation to the solution of the non-linear initial value problem.

x\'=x^2+y

y\'=10-xy

x(1)=0,y(1)=-1

on the interval [1;2] with the step h = 0.2

Please show me the process ^^

Solution

Given x\' = x^2+y we have x1=0, y1= 1 h=0.2, [1, 2] x2 = x1 + h.(x1^2+y1) = 0 + 0.2(1+1) = 0.4 x3 = x2 + h. (x2^2+y2) = 0.4 + 0.2(0.4^2+1.2) = 0.672 for y\' = 10-xy h =0.2 , [1, 2] x1=1 , y1 =1 y2= y1 + h.(x1^2+y1) = 1+ 0.2(1+1) = 1.4 y3 = y2 + h.(x2^2+y2) = 1.4 + 0.2(1.2+1.4) = 1.92