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 = 0.0160879 (sec), leaf count = 81

\[\left \{\left \{y(x)\to \frac {2}{\sqrt {-\frac {1}{x^3}} x^2 \sqrt {-x \left (4 c_1-4 \log (x)+1\right )}+x}\right \},\left \{y(x)\to \frac {2}{\left (-\frac {1}{x^3}\right )^{3/2} x^5 \sqrt {-x \left (4 c_1-4 \log (x)+1\right )}+x}\right \}\right \}\]

Maple : cpu = 0.031 (sec), leaf count = 59

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