2.547   ODE No. 547

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

$$y^{\prime }(x{)}^4-4y(x){(x{y}^{\prime }(x)-2y(x))}^2=0$$ ✓ Mathematica : cpu = 1.29098 (sec), leaf count = 490

$$\{\text{Solve}[\frac{\sqrt{(x^2-4\sqrt{y(x)})y(x)}\log (\sqrt{x^2-4\sqrt{y(x)}}+x)}{\sqrt{x^2-4\sqrt{y(x)}}\sqrt{y(x)}}-\frac{\sqrt{x^2-4\sqrt{y(x)}}\sqrt{y(x)}\log (y(x))}{4\sqrt{(x^2-4\sqrt{y(x)})y(x)}}+\frac{1}{4}\log (y(x))=c_1,y(x)],\text{Solve}[\frac{1}{4}(\frac{\sqrt{x^2-4\sqrt{y(x)}}\sqrt{y(x)}\log (y(x))}{\sqrt{(x^2-4\sqrt{y(x)})y(x)}}+\log (y(x)))-\frac{\sqrt{(x^2-4\sqrt{y(x)})y(x)}\log (\sqrt{x^2-4\sqrt{y(x)}}+x)}{\sqrt{x^2-4\sqrt{y(x)}}\sqrt{y(x)}}=c_1,y(x)],\text{Solve}[\frac{\sqrt{(x^2+4\sqrt{y(x)})y(x)}\log (\sqrt{x^2+4\sqrt{y(x)}}+x)}{\sqrt{x^2+4\sqrt{y(x)}}\sqrt{y(x)}}+\frac{1}{4}(\log (y(x))-\frac{\sqrt{x^2+4\sqrt{y(x)}}\sqrt{y(x)}\log (y(x))}{\sqrt{(x^2+4\sqrt{y(x)})y(x)}})=c_1,y(x)],\text{Solve}[\frac{1}{4}(\frac{\sqrt{x^2+4\sqrt{y(x)}}\sqrt{y(x)}\log (y(x))}{\sqrt{(x^2+4\sqrt{y(x)})y(x)}}+\log (y(x)))-\frac{\sqrt{(x^2+4\sqrt{y(x)})y(x)}\log (\sqrt{x^2+4\sqrt{y(x)}}+x)}{\sqrt{x^2+4\sqrt{y(x)}}\sqrt{y(x)}}=c_1,y(x)]\}$$

✓ Maple : cpu = 0.396 (sec), leaf count = 118

$$\{1\sqrt{y\left(x\right)}{(\sqrt{x^2-4\sqrt{y\left(x\right)}}+x)}^{1\sqrt{x^{2}y\left(x\right)-4{\left(y\left(x\right)\right)}^{3/2}}\frac{1}{\sqrt{x^2-4\sqrt{y\left(x\right)}}}\frac{1}{\sqrt{y\left(x\right)}}}{\left({(\sqrt{x^2-4\sqrt{y\left(x\right)}}-x)}^{1\sqrt{x^{2}y\left(x\right)-4{\left(y\left(x\right)\right)}^{3/2}}\frac{1}{\sqrt{x^2-4\sqrt{y\left(x\right)}}}\frac{1}{\sqrt{y\left(x\right)}}}\right)}^{-1}-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=\frac{x^4}{16}\}$$