2.415   ODE No. 415

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

$$y(x)y^{\prime }(x)+x{y}^{\prime }(x{)}^2-y(x{)}^4=0$$ ✓ Mathematica : cpu = 0.311479 (sec), leaf count = 25

$$\left\{\{y(x)\to \frac{2e^{\frac{c_1}{2}}}{-4x+e^{c_1}}\}\right\}$$ ✓ Maple : cpu = 0.554 (sec), leaf count = 95

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