3.236   ODE No. 236

$$\boxed{{\displaystyle x(y\left(x\right)+4)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-{\left(y\left(x\right)\right)}^2-2y\left(x\right)-2x=0}}$$

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

Mathematica: cpu = 0.015502 (sec), leaf count = 114 $$\{\{y(x)\to \frac{1}{x(\frac{1}{x^2+4x}-\frac{e^{-2(\frac{\log (x)}{4}+\frac{3}{4}\log (x+4))}}{\sqrt{c_1-\frac{4}{x+4}}})}-4\},\{y(x)\to \frac{1}{x(\frac{e^{-2(\frac{\log (x)}{4}+\frac{3}{4}\log (x+4))}}{\sqrt{c_1-\frac{4}{x+4}}}+\frac{1}{x^2+4x})}-4\}\}$$

Maple: cpu = 0.047 (sec), leaf count = 147 $$\{y\left(x\right)=-1(-{(x+4)}^{\frac{3}{2}}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}x+4\mathit{\_}\mathit{C}\mathit{1}-4}{x+4}}x+4x^{3/2}+16\sqrt{x}){({(x+4)}^{\frac{3}{2}}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}x+4\mathit{\_}\mathit{C}\mathit{1}-4}{x+4}}+x^{\frac{3}{2}}+4\sqrt{x})}^{-1},y\left(x\right)=-1({(x+4)}^{\frac{3}{2}}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}x+4\mathit{\_}\mathit{C}\mathit{1}-4}{x+4}}x+4x^{3/2}+16\sqrt{x}){(-{(x+4)}^{\frac{3}{2}}\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}x+4\mathit{\_}\mathit{C}\mathit{1}-4}{x+4}}+x^{\frac{3}{2}}+4\sqrt{x})}^{-1}\}$$