The solution for the following differential eqn :
f''[x]/(1+2f'[x])=(1-Exp[2f[x]]f'[x])(1+Exp[2f[x]]) is
f'[x]=(-Exp[2f[x]]+4f[x]+2(x+C))/(2(1+Exp[2f[x]])). ;where C is constant
Now the differential equation I need to solve is :
f''[x]/(1+2f'[x])=1-f'[x]+(f'[x]-Exp[2f[x]])/(1+Exp[2f[x]](1-Exp(2x)))
I need f'[x]. Mathematica was not able to give a solution to the first differential equation so we had to use some tricks but the trick is not working for the second differential equation. Laplace transform method is also not giving anything. Are there any other(apart from the normal) methods to solve differential equations In Mathematica?