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 = 0.148685 (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 = 0.027 (sec), leaf count = 59

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