2.540   ODE No. 540

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

\[ 2 y(x) y'(x)^3-y(x) y'(x)^2+2 x y'(x)-x=0 \] Mathematica : cpu = 0.0377344 (sec), leaf count = 69

\[\left \{\left \{y(x)\to \frac {x}{2}+c_1\right \},\left \{y(x)\to \frac {\left (3 c_1-2 i x^{3/2}\right ){}^{2/3}}{2^{2/3}}\right \},\left \{y(x)\to \frac {\left (2 i x^{3/2}+3 c_1\right ){}^{2/3}}{2^{2/3}}\right \}\right \}\] Maple : cpu = 0.076 (sec), leaf count = 109

\[\left \{\frac {c_{1} x}{\left (\frac {-x +y \left (x \right )-\sqrt {-x y \left (x \right )}}{y \left (x \right )}\right )^{\frac {2}{3}} \left (\frac {y \left (x \right )+\sqrt {-x y \left (x \right )}}{y \left (x \right )}\right )^{\frac {2}{3}} y \left (x \right )}+x = 0, \frac {c_{1} x}{\left (\frac {-x +y \left (x \right )+\sqrt {-x y \left (x \right )}}{y \left (x \right )}\right )^{\frac {2}{3}} \left (\frac {y \left (x \right )-\sqrt {-x y \left (x \right )}}{y \left (x \right )}\right )^{\frac {2}{3}} y \left (x \right )}+x = 0, y \left (x \right ) = c_{1}+\frac {x}{2}\right \}\]