I tried solving a system of two second order nonlinear ordinary differential equations using the DSolve command. First, I tried like this:

`eqns = {A''[x] == 2/B[x]*A'[x]*B'[x], B''[x] + 1/B[x]*(A'[x])^2 - 1/B[x]*(B'[x])^2 == 0}; sol = DSolve[eqns, {A, B}, x] `

However, as Mathematica didn’t (couldn’t?) solve this, I transformed it into a system of four first order equations:

`eqns = {c'[x] == 2/B[x]*c[x]*d[x], d'[x] + 1/B[x]*(c[x])^2 - 1/B[x]*(d[x])^2 == 0, c[x] == A'[x], d[x] == B'[x], c[0] == 1, d[0] == 1, A[0] == 1, B[0] == 1}; sol = DSolve[eqns, {A, B, c, d}, x] `

This still doesn’t work. Weirdly enough, I don’t even get an error message.

I only included the boundary conditions thinking that they may be helpful, but they aren’t part of my original problem.

Your help would be greatly appreciated:)