3.476   ODE No. 476

$$\boxed{{\displaystyle 9y\left(x\right){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+4x^3\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-4x^{2}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.843107 (sec), leaf count = 454 $$\{\text{Solve}[\frac{\sqrt{x^6+9x^{2}y(x{)}^2}\log (\sqrt{x^4+9y(x{)}^2}+x^2)}{2x\sqrt{x^4+9y(x{)}^2}}+\frac{-x\sqrt{x^4+9y(x{)}^2}\log (y(x{)}^2)+x\sqrt{x^4+9y(x{)}^2}\log (x^4+9y(x{)}^2)-x\sqrt{x^4+9y(x{)}^2}\log (x^5+9xy(x{)}^2)-\sqrt{x^6+9x^{2}y(x{)}^2}\log (\frac{x^4}{9y(x{)}^2}+1)+\sqrt{x^6+9x^{2}y(x{)}^2}\log (\frac{9y(x{)}^2}{x^4}+1)}{4\sqrt{x^6+9x^{2}y(x{)}^2}}=c_1,y(x)],\text{Solve}[\frac{x\sqrt{x^4+9y(x{)}^2}\log (y(x{)}^2)-x\sqrt{x^4+9y(x{)}^2}\log (x^4+9y(x{)}^2)+x\sqrt{x^4+9y(x{)}^2}\log (x^5+9xy(x{)}^2)-\sqrt{x^6+9x^{2}y(x{)}^2}\log (\frac{x^4}{9y(x{)}^2}+1)+\sqrt{x^6+9x^{2}y(x{)}^2}\log (\frac{9y(x{)}^2}{x^4}+1)}{4\sqrt{x^6+9x^{2}y(x{)}^2}}-\frac{\sqrt{x^6+9x^{2}y(x{)}^2}\log (\sqrt{x^4+9y(x{)}^2}+x^2)}{2x\sqrt{x^4+9y(x{)}^2}}=c_1,y(x)]\}$$

Maple: cpu = 0.874 (sec), leaf count = 87 $$\{y\left(x\right)=-\frac{i}{3}{x}^2,y\left(x\right)=\frac{i}{3}{x}^2,y\left(x\right)=-\frac{1}{6}\sqrt{-4x^2\mathit{\_}\mathit{C}\mathit{1}+{\mathit{\_}\mathit{C}\mathit{1}}^2},y\left(x\right)=\frac{1}{6}\sqrt{-4x^2\mathit{\_}\mathit{C}\mathit{1}+{\mathit{\_}\mathit{C}\mathit{1}}^2},y\left(x\right)=-2\frac{\sqrt{x^2\mathit{\_}\mathit{C}\mathit{1}+9}}{\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=2\frac{\sqrt{x^2\mathit{\_}\mathit{C}\mathit{1}+9}}{\mathit{\_}\mathit{C}\mathit{1}}\}$$