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.

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