Hi guys. I'm given the following:

Determine the existence and uniqueness of the solutions of the initial value problem (IVP)

$\displaystyle y'''=(\sin t)e^y+y^2+(y')^{4/3}$,

$\displaystyle y(t_0)=a_0$, $\displaystyle y'(t_0)=a_1$, $\displaystyle y''(t_0)=a_2$.

I really don't know where to begin on this one. Any help would be much appreciated!