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 = 0.0167394 (sec), leaf count = 96

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

Maple : cpu = 0.063 (sec), leaf count = 141

\[ \left \{ y \left ( x \right ) ={1 \left ( - \left ( x+4 \right ) ^{{\frac {3}{2}}}\sqrt {{\frac {{\it \_C1}\, \left ( x+4 \right ) -4}{x+4}}}x-16\,\sqrt {x}-4\,{x}^{3/2} \right ) \left ( - \left ( x+4 \right ) ^{{\frac {3}{2}}}\sqrt {{\frac {{\it \_C1}\, \left ( x+4 \right ) -4}{x+4}}}+4\,\sqrt {x}+{x}^{{\frac {3}{2}}} \right ) ^{-1}},y \left ( x \right ) ={1 \left ( \left ( x+4 \right ) ^{{\frac {3}{2}}}\sqrt {{\frac {{\it \_C1}\, \left ( x+4 \right ) -4}{x+4}}}x-16\,\sqrt {x}-4\,{x}^{3/2} \right ) \left ( \left ( x+4 \right ) ^{{\frac {3}{2}}}\sqrt {{\frac {{\it \_C1}\, \left ( x+4 \right ) -4}{x+4}}}+4\,\sqrt {x}+{x}^{{\frac {3}{2}}} \right ) ^{-1}} \right \} \]