8.143   ODE No. 1733

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

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

Mathematica: cpu = 2.552324 (sec), leaf count = 437 $$\{\{y(x)\to \text{InverseFunction}[-\frac{i\sqrt{2}{\mathrm{\#}\text{1}}^{3/2}\sqrt{\frac{4c_1}{\mathrm{\#}\text{1}(\sqrt{2a{c}_1+b^2}-b)}+2}\sqrt{1-\frac{2c_1}{\mathrm{\#}\text{1}(\sqrt{2a{c}_1+b^2}+b)}}F(i{\sinh }^{-1}\left(\frac{\sqrt{2}\sqrt{\frac{c_1}{\sqrt{b^2+2a{c}_1}-b}}}{\sqrt{\mathrm{\#}\text{1}}}\right)|\frac{b-\sqrt{b^2+2a{c}_1}}{b+\sqrt{b^2+2a{c}_1}})}{\sqrt{\frac{c_1}{\sqrt{2a{c}_1+b^2}-b}}\sqrt{-\mathrm{\#}\text{1}({\mathrm{\#}\text{1}}^{2}a+2\mathrm{\#}\text{1}b-2c_1)}}\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}\left[\frac{i\sqrt{2}{\mathrm{\#}\text{1}}^{3/2}\sqrt{\frac{4c_1}{\mathrm{\#}\text{1}(\sqrt{2a{c}_1+b^2}-b)}+2}\sqrt{1-\frac{2c_1}{\mathrm{\#}\text{1}(\sqrt{2a{c}_1+b^2}+b)}}F(i{\sinh }^{-1}\left(\frac{\sqrt{2}\sqrt{\frac{c_1}{\sqrt{b^2+2a{c}_1}-b}}}{\sqrt{\mathrm{\#}\text{1}}}\right)|\frac{b-\sqrt{b^2+2a{c}_1}}{b+\sqrt{b^2+2a{c}_1}})}{\sqrt{\frac{c_1}{\sqrt{2a{c}_1+b^2}-b}}\sqrt{-\mathrm{\#}\text{1}({\mathrm{\#}\text{1}}^{2}a+2\mathrm{\#}\text{1}b-2c_1)}}\mathrm{\&}\right][c_2+x]\}\}$$

Maple: cpu = 1.560 (sec), leaf count = 71 $$\{{\int }^{y\left(x\right)}-2\frac{1}{\sqrt{-2a{\mathit{\_}\mathit{a}}^3-4b{\mathit{\_}\mathit{a}}^2+4\mathit{\_}\mathit{a}\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}2\frac{1}{\sqrt{-2a{\mathit{\_}\mathit{a}}^3-4b{\mathit{\_}\mathit{a}}^2+4\mathit{\_}\mathit{a}\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$