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## Homework Statement

dx/dt = 2*(1-x^2) with x(0)=0

Obtain the analytic solution to the IVP. Then, obtain the terms in the Taylor series up to and including the t^5 term.

Note: should be possible to express x(t) in terms of hyperbolic functions.

## The Attempt at a Solution

some of my steps;

dx/(1-x^2) = 2dt

*partial fractions + integrated*

0.5[ ln|-x+1| + ln|x+1| ] = 2t + C

-x^2 +1 = A*exp(4t) , A>=0

**x(t)=sqrt(1-exp(4t))**

im not sure if this is right at all, as its simply been a while since I've looked at DE's. If it is right, i can't seem to figure out what combination of hyperbolic functions it relates to! any help would be much appreciated!