Originally Posted by

**shawsend** Ok, I made a mistake. Sorry. Not easy to integrate that. The reason I say that is I just used DSolve in Mathematica and it returns FrenselC functions which is just another name for the integral encountered in this problem but I personally think is ok in terms of an "exact" solution. So then I'd leave it as:

$\displaystyle y=ke^{-\int \sqrt{t}\sin(t) dt}$ or if you wish:

$\displaystyle \int- \sqrt{t}\sin{t} dt=\sqrt{t} \text{Cos}[t]-\sqrt{\frac{\pi }{2}} \text{FresnelC}\left[\sqrt{\frac{2}{\pi }} \sqrt{t}\right]$