Question

consider the initial value problem dy/dx=y^2+1, y(0)=0. estimate y(2)

1) use h=1 to compute your estimate
I got x1=1 x2=2
y=1=1 y2=3
2)use h=1/2 to compute your estimate
I got x1=1/2 x2=1 x3=1.5 x4=2
y1=1/2 y2=9/8 y3=289/128 y4=5.306671143

3) use h=1/8 to compute your answer
there are a lot steps involved here, but I got y 16= 141.22236148

4) what is unusual about your answer? what is going on here and why is it happening?

so my question is why my answers are so different by using differnet value of h? also I don't know how to answer questions 4