Initial condition optimization with discontinuous function.

I have a function:

dx^2/d^2t = ((g + a)/y)*x;

dy^2/d^2t = a;

with a either 0, -5 or 5 depending on the time.

the initial conditions are:

[x0 dx0 y0 dy0] = [? 1.0 1.0 0.0];

where x0 is the variable to find

and the final conditions have to satisfy:

[xf dxf yf dyf] = [0.0 0.0 1.1 0.0];

Which method is the best/fastest to solve this discontinuous problem? I used simulannealbnd,but that seems a bit overkill.

[Torsten]

"a" dependent on time is given or also a control parameter ?