Suppose a tumor of mass $m$ satisfies the differential equation $\frac{dm}{dt}=am^{\frac{3}{4}}-bm-cm^{\frac{2}{3}}$, where $c$ increases slowly from zero. Show that as $c$ increases, the tumour eventually completely disappears.
To do this, I tried sketching a graph of $\frac{dm}{dt}$ but this didn't really yield any results for me.
Hint
Let $m=u^{12}$ to make $$12\,u'\,u^3+b\,u^4-a\,u=-c$$ Switch variables to get $t(u)$ and compute $\partial t/\partial c$ and analyze.