2.926   ODE No. 926

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

\[ y'(x)=\frac {\frac {1}{16} x^3 y(x)^3-\frac {1}{2} x^2 y(x)^3-\frac {3}{8} x^2 y(x)^2+x y(x)^3+x y(x)^2+\frac {3}{4} x y(x)-\frac {1}{2}}{x (x y(x)-2 y(x)-2)} \] Mathematica : cpu = 0.189697 (sec), leaf count = 128

\[\left \{\left \{y(x)\to \frac {2}{x-2}+\frac {1}{16 x (x-2) \left (-\frac {1}{64}-\frac {e^{2 \left (\frac {1}{2} \log (2-x)-\frac {\log (x)}{2}\right )}}{\sqrt {2048 \log (x)+c_1}}\right )}\right \},\left \{y(x)\to \frac {2}{x-2}+\frac {1}{16 x (x-2) \left (-\frac {1}{64}+\frac {e^{2 \left (\frac {1}{2} \log (2-x)-\frac {\log (x)}{2}\right )}}{\sqrt {2048 \log (x)+c_1}}\right )}\right \}\right \}\] Maple : cpu = 0.168 (sec), leaf count = 67

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