# DSolve doesn't give an output for a system of ODEs

I'm trying to solve a system of four ODEs. However, DSolve doesn't give any output (no mistake either).

DSolve[{D[t[s], {s, 2}] == (2 m *D[t[s], s]* D[r[s], s])/(2 m r[s] - r[s]^2),

D[r[s], {s, 2}] == -((m D[r[s], s]^2)/(2 m r[s] - r[s]^2)) + (m (2 m - r[s]) D[t[s], s]^2)/
r[s]^3 - (2 m - r[s]) D[a[s], s]^2 - (2 m - r[s]) Sin[a[s]]^2 D[f[s], s]^2,

D[a[s], {s, 2}] == -((2 D[r[s], s] D[a[s], s])/r[s]) +
Cos[a[s]] Sin[a[s]] D[f[s], s]^2,

D[f[s], {s, 2}] == -((2 (D[r[s], s] + r[s]* Cot[a[s]] D[a[s], s]) D[f[s], s])/
r[s])}, {t[s], r[s], a[s],f[s]}, s] // Simplify


Thank you for any help.

• DSolve cannot solve all ODEs. Generally, it can return only solutions that are listed in existing compendiums of ODE solutions. Few such solutions exist for transcendental ODEs. Try NDSolve for a numerical solution. Jan 4, 2016 at 19:28
• DSolve[D[t[s], {s, 2}] == (2 m*D[t[s], s]*D[r[s], s])/(2 m r[s] - r[s]^2), t[s], s] // FullSimplify can be used to eliminate the first equation, if that helps. Jan 4, 2016 at 19:44