\[ \boxed { a \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{m}+b \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{n}-y \left ( x \right ) =0} \]
Mathematica: cpu = 0.120015 (sec), leaf count = 51 \[ \text {Solve}\left [\left \{x=\frac {a m \text {K$\$$1483716}^{m-1}}{m-1}+\frac {b n \text {K$\$$1483716}^{n-1}}{n-1}+c_1,y(x)=a \text {K$\$$1483716}^m+b \text {K$\$$1483716}^n\right \},\{y(x),\text {K$\$$1483716}\}\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 36 \[ \left \{ x-\int ^{y \left ( x \right ) }\! \left ( {\it RootOf} \left ( -a {{\it \_Z}}^{m}-b{{\it \_Z}}^{n}+{\it \_a} \right ) \right ) ^{-1}{d{ \it \_a}}-{\it \_C1}=0,y \left ( x \right ) =0 \right \} \]