@Rouben Rostamian  

Thank you!

I'll look into that!

@Rouben Rostamian  

Ahhh I see ! Thanks!

If I'm trying to get an answer that met all thoses conditions, could I use the dsolve twice with differents conditions ie. x(0),y(0) and x(1),y(1). Then combine these two together? If I do that, I still get an empty result by using the conditions x(1),y(1),psi(0),D(psi)(0).

eq4:=dsolve({eq1,eq2,eq3,cond1,cond3,cond4,cond5});
eq5:=dsolve({eq1,eq2,eq3,cond2,cond6,cond4,cond5});

I know that an answer that met all of those conditions exist. I'm following a paper and they're using a long analytical approach to solve these equations, but I'm wondering if I can get the same result faster by using dsolve.