2.891   ODE No. 891

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

\[ y'(x)=\frac {y(x)^2 \left (x^4 y(x)+2 x^2 y(x)+2 x^2-2 y(x)\right )}{x^3 \left (x^2 y(x)+x^2-y(x)\right )} \] Mathematica : cpu = 0.166652 (sec), leaf count = 135

\[\left \{\left \{y(x)\to \frac {x^5}{-x^3 \left (x^2-1\right )+\frac {\sqrt {\left (x^2-1\right )^2 x+x^5 \left (-2 \left (-\frac {1}{x^2}+\frac {1}{2 x^4}+\log (x)\right )+c_1\right )}}{\sqrt {\frac {1}{x^5}}}}\right \},\left \{y(x)\to -\frac {x^5}{\left (x^2-1\right ) x^3+\frac {\sqrt {\left (x^2-1\right )^2 x+x^5 \left (-2 \left (-\frac {1}{x^2}+\frac {1}{2 x^4}+\log (x)\right )+c_1\right )}}{\sqrt {\frac {1}{x^5}}}}\right \}\right \}\] Maple : cpu = 0.165 (sec), leaf count = 56

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