A few issues:
1) I doubt DSolve will be able to solve this system of equations. You should try NDSolve, as well as set an initial and final time: e.g. {t, 0, 1}
2) Inside of your notebook, u[t]= should probably be u[t_] :=
3) From a scientific viewpoint: do you have "Terminal Conditions" to make a BVP rather than an IVP? These are often found in Pontryagin-type problems, often solved with the Shooting Method of NDSolve.
