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