Forgive me if I am wrong, but it may simply be impossible without knowing the function y(t).

dx = a sin(y(t)) dt

Let us just call the funtion "ƒ" instead of y:

dx = a sin(ƒ(t)) dt

If, *for example*, there were no sine or factor applied, we could have:

dx = ƒ(t) dt

Which is just a general statement.

So, yes, what is y(t) ?