3.85   ODE No. 85

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-x^{a-1}{\left(y\left(x\right)\right)}^{1-b}f(\frac{x^a}{a}+\frac{{\left(y\left(x\right)\right)}^b}{b})=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 155.676769 (sec), leaf count = 235 $$\text{Solve}[{\int }_1^{y(x)}(-{\int }_1^x(\frac{K[1{]}^{a-1}K[2{]}^{b-1}{f}^{\prime }(\frac{K[1{]}^a}{a}+\frac{K[2{]}^b}{b})}{f(\frac{K[1{]}^a}{a}+\frac{K[2{]}^b}{b})+1}-\frac{K[1{]}^{a-1}K[2{]}^{b-1}f(\frac{K[1{]}^a}{a}+\frac{K[2{]}^b}{b})f^{\prime }(\frac{K[1{]}^a}{a}+\frac{K[2{]}^b}{b})}{{(f(\frac{K[1{]}^a}{a}+\frac{K[2{]}^b}{b})+1)}^2})dK[1]-\frac{K[2{]}^{b-1}}{f(\frac{K[2{]}^b}{b}+\frac{x^a}{a})+1})dK[2]+{\int }_1^x\frac{K[1{]}^{a-1}f(\frac{K[1{]}^a}{a}+\frac{y(x{)}^b}{b})}{f(\frac{K[1{]}^a}{a}+\frac{y(x{)}^b}{b})+1}dK[1]=c_1,y(x)]$$

Maple: cpu = 0.359 (sec), leaf count = 153 $$\{y\left(x\right)=\sqrt[b]{-\frac{1}{a}(-\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}{({\left(\sqrt[a]{a}\right)}^{a}f\left(\frac{{\left(\sqrt[a]{a}\right)}^{a}b+{\left(\sqrt[b]{-b+\mathit{\_}\mathit{a}}\right)}^{b}a}{ab}\right){\left(\sqrt[b]{-b+\mathit{\_}\mathit{a}}\right)}^{-b}\mathit{\_}\mathit{a}-{\left(\sqrt[a]{a}\right)}^{a}f\left(\frac{{\left(\sqrt[a]{a}\right)}^{a}b+{\left(\sqrt[b]{-b+\mathit{\_}\mathit{a}}\right)}^{b}a}{ab}\right){\left(\sqrt[b]{-b+\mathit{\_}\mathit{a}}\right)}^{-b}b+a)}^{-1}d\mathit{\_}\mathit{a}{a}^2+\mathit{\_}\mathit{C}\mathit{1}ab-x^{a}b)a+x^{a}b)}\}$$