8.130   ODE No. 1720

$$\boxed{{\displaystyle \left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)+a{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+b{\left(y\left(x\right)\right)}^2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+c{\left(y\left(x\right)\right)}^4=0}}$$

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

Mathematica: cpu = 89.226830 (sec), leaf count = 38 $$\text{DSolve}[a{y}^{\prime }(x{)}^2+by(x{)}^2{y}^{\prime }(x)+cy(x{)}^4+y(x)y^{″}(x)=0,y(x),x]$$

Maple: cpu = 1.747 (sec), leaf count = 174 $$\{{\int }^{y\left(x\right)}(2a+4){(\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(2\mathit{\_}\mathit{Z}b{\mathit{\_}\mathit{a}}^2-2a\ln \left(\mathit{\_}\mathit{a}\right)\sqrt{{\mathit{\_}\mathit{a}}^4(4ac-b^2+8c)}-\ln \left(\frac{{\mathit{\_}\mathit{a}}^4(4ac{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2-b^2{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+8c{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+4ac-b^2+8c)}{4a+8}\right)\sqrt{{\mathit{\_}\mathit{a}}^4(4ac-b^2+8c)}+\mathit{\_}\mathit{C}\mathit{1}\sqrt{{\mathit{\_}\mathit{a}}^4(4ac-b^2+8c)})\right)\sqrt{{\mathit{\_}\mathit{a}}^4(4ac-b^2+8c)}-b{\mathit{\_}\mathit{a}}^2)}^{-1}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$