2.236   ODE No. 236

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

\[ x (y(x)+4) y'(x)-y(x)^2-2 y(x)-2 x=0 \] Mathematica : cpu = 0.238047 (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 = 0.065 (sec), leaf count = 141

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