3.470   ODE No. 470

$$\boxed{{\displaystyle y\left(x\right){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+x^3\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-x^{2}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.883112 (sec), leaf count = 454 $$\{\text{Solve}[\frac{\sqrt{x^6+4x^{2}y(x{)}^2}\log (\sqrt{x^4+4y(x{)}^2}+x^2)}{2x\sqrt{x^4+4y(x{)}^2}}+\frac{-x\sqrt{x^4+4y(x{)}^2}\log (y(x{)}^2)+x\sqrt{x^4+4y(x{)}^2}\log (x^4+4y(x{)}^2)-x\sqrt{x^4+4y(x{)}^2}\log (x^5+4xy(x{)}^2)-\sqrt{x^6+4x^{2}y(x{)}^2}\log (\frac{x^4}{4y(x{)}^2}+1)+\sqrt{x^6+4x^{2}y(x{)}^2}\log (\frac{4y(x{)}^2}{x^4}+1)}{4\sqrt{x^6+4x^{2}y(x{)}^2}}=c_1,y(x)],\text{Solve}[\frac{x\sqrt{x^4+4y(x{)}^2}\log (y(x{)}^2)-x\sqrt{x^4+4y(x{)}^2}\log (x^4+4y(x{)}^2)+x\sqrt{x^4+4y(x{)}^2}\log (x^5+4xy(x{)}^2)-\sqrt{x^6+4x^{2}y(x{)}^2}\log (\frac{x^4}{4y(x{)}^2}+1)+\sqrt{x^6+4x^{2}y(x{)}^2}\log (\frac{4y(x{)}^2}{x^4}+1)}{4\sqrt{x^6+4x^{2}y(x{)}^2}}-\frac{\sqrt{x^6+4x^{2}y(x{)}^2}\log (\sqrt{x^4+4y(x{)}^2}+x^2)}{2x\sqrt{x^4+4y(x{)}^2}}=c_1,y(x)]\}$$

Maple: cpu = 0.780 (sec), leaf count = 87 $$\{y\left(x\right)=-\frac{i}{2}{x}^2,y\left(x\right)=\frac{i}{2}{x}^2,y\left(x\right)=-\frac{1}{4}\sqrt{-4x^2\mathit{\_}\mathit{C}\mathit{1}+{\mathit{\_}\mathit{C}\mathit{1}}^2},y\left(x\right)=\frac{1}{4}\sqrt{-4x^2\mathit{\_}\mathit{C}\mathit{1}+{\mathit{\_}\mathit{C}\mathit{1}}^2},y\left(x\right)=-2\frac{\sqrt{x^2\mathit{\_}\mathit{C}\mathit{1}+4}}{\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=2\frac{\sqrt{x^2\mathit{\_}\mathit{C}\mathit{1}+4}}{\mathit{\_}\mathit{C}\mathit{1}}\}$$