I tried using
NDSolve to solve the following system of equations:
t x'[t] == -x[t] + y[t], t y'[t] == -5 t^2/x[t]^2 + x[t] - y[t], x == 4, x == 1
It's weird. The system tells me there is infinity at the boundary $t=1$, so I change the boundary from $t=1$ to $t=2$, and I get the same message again.
If I eliminate the nonlinear term
-5 t^2/x[t]^2, the function can be solved analytically. So I do not know whether these equations are well posed or not with such boundary conditions just for
Anyone have a suggestion?