3.954   ODE No. 954

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{150x^3+125\sqrt{x}+125+125{\left(y\left(x\right)\right)}^2-100x^{3}y\left(x\right)-500y\left(x\right)\sqrt{x}+20x^6+200x^{7/2}+500x+125{\left(y\left(x\right)\right)}^3-150x^3{\left(y\left(x\right)\right)}^2-750{\left(y\left(x\right)\right)}^2\sqrt{x}+60y\left(x\right)x^6+600y\left(x\right)x^{7/2}+1500xy\left(x\right)-8x^9-120x^{13/2}-600x^4-1000x^{3/2}}{125x}=0}}$$

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

Mathematica: cpu = 0.087511 (sec), leaf count = 115 $$\text{Solve}[-\frac{29}{3}\text{RootSum}[-29{\mathrm{\#}\text{1}}^3+3\sqrt[3]{29}\mathrm{\#}\text{1}-29\mathrm{\&},\frac{\log (\frac{\frac{-6x^3-30\sqrt{x}+5}{5x}+\frac{3y(x)}{x}}{\sqrt[3]{29}\sqrt[3]{\frac{1}{x^3}}}-\mathrm{\#}\text{1})}{\sqrt[3]{29}-29{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{1}{9}{29}^{2/3}{\left(\frac{1}{x^3}\right)}^{2/3}{x}^2\log (x),y(x)]$$

Maple: cpu = 0.031 (sec), leaf count = 53 $$\{y\left(x\right)=\frac{1}{45}(18x^{7/2}+145\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-81{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+\ln \left(x\right)+3\mathit{\_}\mathit{C}\mathit{1})\sqrt{x}-15\sqrt{x}+90x)\frac{1}{\sqrt{x}}\}$$