2.236   ODE No. 236

\[ x (y(x)+4) y'(x)-y(x)^2-2 y(x)-2 x=0 \]

✓ Mathematica : cpu = 0.0913848 (sec), leaf count = 114

DSolve[-2*x - 2*y[x] - y[x]^2 + x*(4 + y[x])*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -4+\frac {1}{x \left (\frac {1}{x^2+4 x}-\frac {e^{-2 \left (\frac {\log (x)}{4}+\frac {3}{4} \log (x+4)\right )}}{\sqrt {-\frac {4}{x+4}+c_1}}\right )}\right \},\left \{y(x)\to -4+\frac {1}{x \left (\frac {1}{x^2+4 x}+\frac {e^{-2 \left (\frac {\log (x)}{4}+\frac {3}{4} \log (x+4)\right )}}{\sqrt {-\frac {4}{x+4}+c_1}}\right )}\right \}\right \}\]

✓ Maple : cpu = 0.085 (sec), leaf count = 141

dsolve(x*(y(x)+4)*diff(y(x),x)-y(x)^2-2*y(x)-2*x = 0,y(x))
 

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