2.1779   ODE No. 1779

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

$$ax+y(x{)}^2{y}^{″}(x)+y(x)y^{\prime }(x{)}^2=0$$ ✗ Mathematica : cpu = 3.64357 (sec), leaf count = 0 , could not solve

DSolve[a*x + y[x]*Derivative[1][y][x]^2 + y[x]^2*Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.585 (sec), leaf count = 112

$$\{\ln \left(x\right)-{\int }^{\frac{y\left(x\right)}{x}}\frac{{\mathit{\_}\mathit{g}}^2}{2{\mathit{\_}\mathit{g}}^3+2a}(\sqrt[3]{\frac{a}{{\mathit{\_}\mathit{g}}^3}}\sqrt{3}\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2\mathit{\_}\mathit{Z}\sqrt{3}+\ln \left(\frac{{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+1}{3+2\sqrt{3}\tan \left(\mathit{\_}\mathit{Z}\right)+{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2}\right)+6\mathit{\_}\mathit{C}\mathit{1}+6\int \frac{{\mathit{\_}\mathit{g}}^2}{{\mathit{\_}\mathit{g}}^3+a}{\left(\frac{a}{{\mathit{\_}\mathit{g}}^3}\right)}^{2/3}\mathrm{d}\mathit{\_}\mathit{g})\right)+\sqrt[3]{\frac{a}{{\mathit{\_}\mathit{g}}^3}}-2)d\mathit{\_}\mathit{g}-\mathit{\_}\mathit{C}\mathit{2}=0\}$$