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## 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 at a Solution

y_n=cosh(4x^2-2y^2)

y''= (cosh(4x^2-2y^2)(4/3x^3-2/3y^3)

y_0=14

y_n+1=y_n+h{y_ncosh(4x_n^2-2y_n^2)+h^2/2[cosh(4x_n^2-2y_n^2)(4/3x_n^3-2/3y_n^3)]

I'm pretty sure I'm doing this wrong, and I also have no idea how to go about writing a computer program to do this work