2.260   ODE No. 260

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

\[ \left (2 x^2 y(x)+x\right ) y'(x)-x^2 y(x)^3+2 x y(x)^2+y(x)=0 \] Mathematica : cpu = 0.114147 (sec), leaf count = 80

\[\left \{\left \{y(x)\to \frac {x}{-2 x^2+\frac {\sqrt {4 x+x (-2 \log (x)+c_1)}}{\sqrt {\frac {1}{x^3}}}}\right \},\left \{y(x)\to -\frac {x}{2 x^2+\frac {\sqrt {4 x+x (-2 \log (x)+c_1)}}{\sqrt {\frac {1}{x^3}}}}\right \}\right \}\] Maple : cpu = 0.023 (sec), leaf count = 59

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