2.254   ODE No. 254

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

\[ x^2 y(x)^3+x (x y(x)-2) y'(x)+x y(x)^2-2 y(x)=0 \] Mathematica : cpu = 0.123539 (sec), leaf count = 99

\[\left \{\left \{y(x)\to -\frac {2 x}{-x^2+\frac {\sqrt {2} \sqrt {-\frac {x}{2}-2 x (-\log (x)+c_1)}}{\sqrt {-\frac {1}{x^3}}}}\right \},\left \{y(x)\to \frac {2 x}{x^2+\frac {\sqrt {2} \sqrt {-\frac {x}{2}-2 x (-\log (x)+c_1)}}{\sqrt {-\frac {1}{x^3}}}}\right \}\right \}\] Maple : cpu = 0.022 (sec), leaf count = 59

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