2.888   ODE No. 888

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

\[ y'(x)=\frac {x^4 y(x)^3-5 x^3 y(x)^2+6 x^2 y(x)-2 x y(x)-2 x+1}{x^2 \left (x^2 y(x)-x+1\right )} \] Mathematica : cpu = 0.153244 (sec), leaf count = 78

\[\left \{\left \{y(x)\to \frac {x-1}{x^2}+\frac {1}{x^4 \left (\frac {1}{x^2}-\frac {1}{x^2 \sqrt {\frac {2}{x}+c_1}}\right )}\right \},\left \{y(x)\to \frac {x-1}{x^2}+\frac {1}{x^4 \left (\frac {1}{x^2}+\frac {1}{x^2 \sqrt {\frac {2}{x}+c_1}}\right )}\right \}\right \}\] Maple : cpu = 0.168 (sec), leaf count = 79

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