2.400   ODE No. 400

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

$$-2x^2{y}^{\prime }(x)+2y^{\prime }(x{)}^2+3xy(x)=0$$ ✓ Mathematica : cpu = 0.252126 (sec), leaf count = 135

$$\{\text{Solve}[\frac{1}{3}\log (y(x))-\frac{2\sqrt{x^4-6xy(x)}{\tanh }^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-6y(x)}}\right)}{3\sqrt{x}\sqrt{x^3-6y(x)}}=c_1,y(x)],\text{Solve}[\frac{2\sqrt{x^4-6xy(x)}{\tanh }^{-1}\left(\frac{x^{3/2}}{\sqrt{x^3-6y(x)}}\right)}{3\sqrt{x}\sqrt{x^3-6y(x)}}+\frac{1}{3}\log (y(x))=c_1,y(x)]\}$$ ✓ Maple : cpu = 0.339 (sec), leaf count = 74

$$\{y\left(x\right)=\frac{x^3}{6},y\left(x\right)=\frac{1}{3\mathit{\_}\mathit{C}\mathit{1}}(-\sqrt{-6\mathit{\_}\mathit{C}\mathit{1}x}x+3),y\left(x\right)=\frac{1}{3\mathit{\_}\mathit{C}\mathit{1}}(\sqrt{-6\mathit{\_}\mathit{C}\mathit{1}x}x+3),y\left(x\right)=-\frac{x}{3}\sqrt{-6\mathit{\_}\mathit{C}\mathit{1}x}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\frac{x}{3}\sqrt{-6\mathit{\_}\mathit{C}\mathit{1}x}+\mathit{\_}\mathit{C}\mathit{1}\}$$