It looks like I am making a calculus mistake here, and I am really banging my head against the wall.
Here is my work:
I know I should be getting $dY/dT=-(MPC)/(1-MPC)$, where $MPC=dC/dY$ If this is at all helpful here is a picture of page 295 in 7th edition of Macroeconomics By Mankiw that briefly describes the process.
It is confusing to me that he uses $C'$ for both terms on right-hand side when $C$ is composed of two arguments, so I decided to use Leibniz notation to see what is going on.
Thanks for help! Chris