Thanks for the help Theo, but my problem now lies in the programming bit of the problem. I think I've got the steps before it figured out. Please correct me if I'm wrong.
y''= x3(y^2)y' + y^3 -[(-sin(x)siny) + (cos(x)cos(y)y')]
= 3x(y^2)y' + y^3 +[cos(x)cos(y)y' - sin(x)sin(y)]
y'=...
wow, my professor changed the IVP to:
y'=xy^3 - cos(x)sin(y)
y(0)= -1
still using h= .1 and looking for y_1 to y_20, as well as writing the program. Apparently the original blew up too quickly.
Homework Statement
Use the "Three Term" Taylor's approximation to find approximate values y_1 through y_20 with h=.1 for this Initial Value Problem:
y'= cosh(4x^2-2y^2)
y(0)=14
And write a computer program to do the grunt work approximation
Homework Equations
The Attempt...