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 = 0.411392 (sec), leaf count = 143

$$\{\text{Solve}[-\frac{x\sqrt{x^{4}y(x)+4}y(x{)}^{3/2}{\sinh }^{-1}\left(\frac{1}{2}{x}^2\sqrt{y(x)}\right)}{2\sqrt{x^{2}y(x{)}^3(x^{4}y(x)+4)}}-\frac{1}{4}\log (y(x))=c_1,y(x)],\text{Solve}[\frac{xy(x{)}^{3/2}\sqrt{x^{4}y(x)+4}{\sinh }^{-1}\left(\frac{1}{2}{x}^2\sqrt{y(x)}\right)}{2\sqrt{x^{2}y(x{)}^3(x^{4}y(x)+4)}}-\frac{1}{4}\log (y(x))=c_1,y(x)]\}$$ ✓ Maple : cpu = 0.802 (sec), leaf count = 128

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