2.1843   ODE No. 1843

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

$$-y^{\prime }(x)y^{″}(x)+y(x{)}^3{y}^{\prime }(x)+y^{(3)}(x)y(x)=0$$ ✓ Mathematica : cpu = 2.00802 (sec), leaf count = 409

$$\{\{y(x)\to \text{InverseFunction}[-\frac{2i\sqrt{1+\frac{{\mathrm{\#}\text{1}}^2}{2(\sqrt{c_2{}^2-c_1}-c_2)}}\sqrt{1-\frac{{\mathrm{\#}\text{1}}^2}{2(c_2+\sqrt{c_2{}^2-c_1})}}F(i{\sinh }^{-1}\left(\frac{\sqrt{\frac{1}{\sqrt{c_2{}^2-c_1}-c_2}}\mathrm{\#}\text{1}}{\sqrt{2}}\right)|\frac{c_2-\sqrt{c_2{}^2-c_1}}{c_2+\sqrt{c_2{}^2-c_1}})}{\sqrt{\frac{1}{\sqrt{c_2{}^2-c_1}-c_2}}\sqrt{-\frac{{\mathrm{\#}\text{1}}^4}{2}+2{\mathrm{\#}\text{1}}^2{c}_2-2c_1}}\mathrm{\&}][x+c_3]\},\{y(x)\to \text{InverseFunction}\left[\frac{2i\sqrt{1+\frac{{\mathrm{\#}\text{1}}^2}{2(\sqrt{c_2{}^2-c_1}-c_2)}}\sqrt{1-\frac{{\mathrm{\#}\text{1}}^2}{2(c_2+\sqrt{c_2{}^2-c_1})}}F(i{\sinh }^{-1}\left(\frac{\sqrt{\frac{1}{\sqrt{c_2{}^2-c_1}-c_2}}\mathrm{\#}\text{1}}{\sqrt{2}}\right)|\frac{c_2-\sqrt{c_2{}^2-c_1}}{c_2+\sqrt{c_2{}^2-c_1}})}{\sqrt{\frac{1}{\sqrt{c_2{}^2-c_1}-c_2}}\sqrt{-\frac{{\mathrm{\#}\text{1}}^4}{2}+2{\mathrm{\#}\text{1}}^2{c}_2-2c_1}}\mathrm{\&}\right][x+c_3]\}\}$$ ✓ Maple : cpu = 0.596 (sec), leaf count = 77

$$\{{\int }^{y\left(x\right)}-2\frac{1}{\sqrt{-{\mathit{\_}\mathit{a}}^4+4\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2-4{\mathit{\_}\mathit{C}\mathit{2}}^2+4\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{3}=0,{\int }^{y\left(x\right)}2\frac{1}{\sqrt{-{\mathit{\_}\mathit{a}}^4+4\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2-4{\mathit{\_}\mathit{C}\mathit{2}}^2+4\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{3}=0\}$$