ODE No. 876

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

\[ y'(x)=-\frac {y(x)^2 \left (x^2 y(x)-2 x y(x)+y(x)-2 x\right )}{2 x (x y(x)-2 y(x)-2)} \] Mathematica : cpu = 0.0193312 (sec), leaf count = 135

\[\left \{\left \{y(x)\to -\frac {4 x}{\frac {2 \sqrt {-4 x \left (c_1-2 \left (\frac {x^2}{8}-\frac {x}{2}+\frac {\log (x)}{4}\right )\right )-x (x-2)^2}}{\sqrt {-\frac {1}{x}}}-2 (x-2) x}\right \},\left \{y(x)\to \frac {4 x}{\frac {2 \sqrt {-4 x \left (c_1-2 \left (\frac {x^2}{8}-\frac {x}{2}+\frac {\log (x)}{4}\right )\right )-x (x-2)^2}}{\sqrt {-\frac {1}{x}}}+2 (x-2) x}\right \}\right \}\] Maple : cpu = 0.059 (sec), leaf count = 41

\[ \left \{ y \left ( x \right ) =-4\, \left ( \sqrt {{\it \_C1}-8\,\ln \left ( x \right ) }-2\,x+4 \right ) ^{-1},y \left ( x \right ) =4\, \left ( \sqrt {{\it \_C1}-8\,\ln \left ( x \right ) }+2\,x-4 \right ) ^{-1} \right \} \]