8.190   ODE No. 1780

$$\boxed{{\displaystyle {\left(y\left(x\right)\right)}^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+y\left(x\right){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-ax-b=0}}$$

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

Mathematica: cpu = 0.488562 (sec), leaf count = 32 $$\text{DSolve}[-ax-b+y(x{)}^2{y}^{″}(x)+y(x)y^{\prime }(x{)}^2=0,y(x),x]$$

Maple: cpu = 2.012 (sec), leaf count = 172 $$\{\frac{b\ln (ax+b)}{a}-{\int }^{\frac{y\left(x\right)}{ax+b}}\frac{1}{2\sqrt{3}{\mathit{\_}\mathit{g}}^3{a}^2-2\sqrt{3}}(3b^2{\mathit{\_}\mathit{g}}^2\sqrt[3]{-\frac{a}{{\mathit{\_}\mathit{g}}^3{b}^3}}\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(6b^2\int \frac{{\mathit{\_}\mathit{g}}^2}{{\mathit{\_}\mathit{g}}^3{a}^2-1}{(-\frac{a}{{\mathit{\_}\mathit{g}}^3{b}^3})}^{2/3}\mathrm{d}\mathit{\_}\mathit{g}-2\mathit{\_}\mathit{Z}\sqrt{3}+\ln \left(\frac{{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+1}{3+2\sqrt{3}\tan \left(\mathit{\_}\mathit{Z}\right)+{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2}\right)+6\mathit{\_}\mathit{C}\mathit{1})\right)+b^2{\mathit{\_}\mathit{g}}^2\sqrt[3]{-\frac{a}{{\mathit{\_}\mathit{g}}^3{b}^3}}\sqrt{3}-2{\mathit{\_}\mathit{g}}^{2}ab\sqrt{3})d\mathit{\_}\mathit{g}-\mathit{\_}\mathit{C}\mathit{2}=0\}$$