2.397   ODE No. 397

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

$$-2x^{3}y(x{)}^2{y}^{\prime }(x)-4x^{2}y(x{)}^3+y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 0.669461 (sec), leaf count = 136

$$\{\text{Solve}[4c_1+\frac{2x\sqrt{x^{4}y(x)+4}y(x{)}^{3/2}{\sinh }^{-1}\left(\frac{1}{2}{x}^2\sqrt{y(x)}\right)}{\sqrt{x^{2}y(x{)}^3(x^{4}y(x)+4)}}+\log (y(x))=0,y(x)],\text{Solve}[4c_1+\log (y(x))=\frac{2xy(x{)}^{3/2}\sqrt{x^{4}y(x)+4}{\sinh }^{-1}\left(\frac{1}{2}{x}^2\sqrt{y(x)}\right)}{\sqrt{x^{2}y(x{)}^3(x^{4}y(x)+4)}},y(x)]\}$$

✓ Maple : cpu = 0.977 (sec), leaf count = 128

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