2.236   ODE No. 236

\[ x (y(x)+4) y'(x)-y(x)^2-2 y(x)-2 x=0 \] Mathematica : cpu = 0.126611 (sec), leaf count = 114


\[\left \{\left \{y(x)\to -4+\frac {1}{x \left (\frac {1}{x^2+4 x}-\frac {e^{-2 \left (\frac {\log (x)}{4}+\frac {3}{4} \log (x+4)\right )}}{\sqrt {-\frac {4}{x+4}+c_1}}\right )}\right \},\left \{y(x)\to -4+\frac {1}{x \left (\frac {1}{x^2+4 x}+\frac {e^{-2 \left (\frac {\log (x)}{4}+\frac {3}{4} \log (x+4)\right )}}{\sqrt {-\frac {4}{x+4}+c_1}}\right )}\right \}\right \}\] Maple : cpu = 0.063 (sec), leaf count = 141


\[y \relax (x ) = \frac {-\left (x +4\right )^{\frac {3}{2}} \sqrt {\frac {c_{1} \left (x +4\right )-4}{x +4}}\, x -16 \sqrt {x}-4 x^{\frac {3}{2}}}{-\left (x +4\right )^{\frac {3}{2}} \sqrt {\frac {c_{1} \left (x +4\right )-4}{x +4}}+4 \sqrt {x}+x^{\frac {3}{2}}}\]