Verifying the solution to an ODE

I was working on solving a partial differential equation and I reduced it to an ODE, namely $\displaystyle \frac{-T(t)}{2t} = \frac{\partial T}{\partial t}$. I know the answer is $\displaystyle T(t) = \frac{1}{\sqrt{t}}$, which works as a solution, however I'm really rusty and don't know what a good way to tackle solving the ODE is. I tried digging out my old laplace transforms tables but I'm hitting a brick wall.

Any suggestions?

Anthony

Re: Verifying the solution to an ODE

Re: Verifying the solution to an ODE

I'm totally blind, thank you so much haha