first order ODE, Fresnel integral?

for this ODE-$\displaystyle \frac{dy}{dt}+y\sqrt{t}sint=0$, do I need to use a Fresnel integral to solve it? or can it be simplified another way from the standard form y(t)=cexp(-I)? it can be expanded to the expression- $\displaystyle \large y(t)=ce^{\sqrt{2}cost+\frac{1}{2}\int \frac{cost}{\sqrt{t}}dt}$

thanks very much!

Re: first order ODE, Fresnel integral?

Hey mathlover10.

You should be able to use an integrating factor or a simple separation of variables to solve this DE.

Re: first order ODE, Fresnel integral?

Hi mathlover10 !

Any method used to solve the ODE will not change the result. If one method leads to a Fresnel integral, do not expect something else from another method.

If you don't want a closed form, such as a Fresnel integral, it's up to you to search an infinite series instead of.