I have two coupled non linear second order differential equation.
-y1''[x] == + Exp[k1 (y1[x] - y2[x])] - Exp[-k2 (y1[x] - y2[x])], -y2''[x] == - Exp[k1 (y1[x] - y2[x])] + Exp[-k2 (y1[x] - y2[x])]
I have been trying to solve it for past two weeks. Of course, I could get the numeric solution, but I am not able to get analytical solution. So, I was wondering if someone could help me how to solve this analytically so that I can get solution in terms of
y2. Any solution to this problem would be of interest.
I am completely new to Mathematica, so any example worksheets on this sort of equation would be gratefully appreciated!