*** This is my interpretation of the problem:
x=x(t)
y=y(t)

dx=a.sin(y(t))dt

I want to solve this for x.

dx/dt = a.sin( y(t) )
∫ (dx/dt)dt = ∫a.sin( y(t) )dt
∫ dx = ∫a.sin( y(t) )dt
x(t)+C=∫a.sin( y(t) )dt

*** if..
y(t)=a.t
      then
dy/dt=a

*** therefore...
∫a.sin( y(t) )dt = ∫a.sin( a.t) )dt
Let z=a.t => dz/dt = a
∫a.sin( a.t) )dt = ∫(dz/dt)sin(z)dt = ∫sin(z)dz = -cos(z)+C = -cos(a.t)+C

*** putting it all together...
x(t) = -cos(a.t)+C
y(t)= a.t

dx/dt= a.sin(a.t)
dx= a.sin(a.t) dt
dx=a sin(y(t)) dt <=> dx=a sin(y) dt

***I think this is a possible solution for your problem

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) ?

I'm not convinced... i dont get it really. Do you mead x = a(-cos(yt/y)) ?
How do i differentiate that one and get the same thing in the brickets sin(y).
Ganesh... maybe i didn't make my self clear that y is a function of t.?? Or is it
me that have misunderstood you? Coud you show me how you diferentiate the
expression?

Hi guys, I'm stuck again!
And it's mathematical, like always (regret those lazy days back in analytic math courses, haha).

I'm in this situation:

dx=asin(y)dt

(a is a constant value)

where y=y(t)

I want to solve this for x.
smthing like x = smthing + C (constant of integration, or what ever you want to call it)

I can recall it had something to do about, maybe substitution, but i can't see how thats going to happen...