I need help with this problem!

An object moving along a curve in the xy-plane has position [x(t), y(t)] with dx/dt=cos(t^2) and dy/dt=sin(t^3). At time t=0, the particle is at position (4,7). Where is the particle when t=2?

I can get the integrals of both equations, but my problem is that when I try to substitute t=0 to find the constants of integration, it becomes undefined. Help!

This is what I end up with:

X=[sin(t^2)]/(2t)+C

Y=[(-cos(t^3)]/(3t^2)+C

But then you can't substitute t=0, or am I missing something? Probably am