Question

This question is pretty hard...

Solve the problem (that is, estimate y(0.4)) by keeping the first 5 terms in the Taylor series method.

dy/dx=f(x,y), y(x0)=y0

f(x,y)=2x−y^2 , y(0)=1

Expand y(x) in Taylor’s series around x = 0:

y(x)=y(0)+xy′(0)+((x^2)y′′(0))/2+(x^3y′′′(0))/6+ (x^4y''''(0))/24+...