\[ \text {Global$\grave { }$x}^{\text {Global$\grave { }$n}} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^{\text {Global$\grave { }$m}} \left (\text {Global$\grave { }$a} \text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+\text {Global$\grave { }$b} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right )+\text {Global$\grave { }$alpha} \text {Global$\grave { }$x} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})+\text {Global$\grave { }$beta} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})=0 \] ✓ Mathematica : cpu = 0.320948 (sec), leaf count = 102
\[\text {Solve}\left [\frac {\text {Global$\grave { }$m} \left ((\text {Global$\grave { }$a} \text {Global$\grave { }$beta}-\text {Global$\grave { }$alpha} \text {Global$\grave { }$b}) \log \left (\text {Global$\grave { }$x}^{\text {Global$\grave { }$n}} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^{\text {Global$\grave { }$m}} (\text {Global$\grave { }$b} \text {Global$\grave { }$m}-\text {Global$\grave { }$a} \text {Global$\grave { }$n})-\text {Global$\grave { }$alpha} \text {Global$\grave { }$n}+\text {Global$\grave { }$beta} \text {Global$\grave { }$m}\right )+\text {Global$\grave { }$beta} \log (\text {Global$\grave { }$x}) (\text {Global$\grave { }$b} \text {Global$\grave { }$m}-\text {Global$\grave { }$a} \text {Global$\grave { }$n})\right )}{(\text {Global$\grave { }$b} \text {Global$\grave { }$m}-\text {Global$\grave { }$a} \text {Global$\grave { }$n}) (\text {Global$\grave { }$beta} \text {Global$\grave { }$m}-\text {Global$\grave { }$alpha} \text {Global$\grave { }$n})}+\frac {\text {Global$\grave { }$alpha} \text {Global$\grave { }$m} \log (\text {Global$\grave { }$beta} \text {Global$\grave { }$m} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})-\text {Global$\grave { }$alpha} \text {Global$\grave { }$n} \text {Global$\grave { }$y}(\text {Global$\grave { }$x}))}{\text {Global$\grave { }$beta} \text {Global$\grave { }$m}-\text {Global$\grave { }$alpha} \text {Global$\grave { }$n}}=c_1,\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ]\]
✓ Maple : cpu = 0.401 (sec), leaf count = 78
\[ \left \{ {x}^{a\beta \,mn-b\beta \,{m}^{2}} \left ( \left ( y \left ( x \right ) \right ) ^{m} \right ) ^{a\alpha \,n-\alpha \,bm} \left ( {x}^{n}n \left ( y \left ( x \right ) \right ) ^{m}a-{x}^{n} \left ( y \left ( x \right ) \right ) ^{m}mb+\alpha \,n-\beta \,m \right ) ^{-a\beta \,m+\alpha \,bm}-{\it \_C1}=0 \right \} \]