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 = 0.145263 (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 = 0.029 (sec), leaf count = 59

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