2.1766   ODE No. 1766

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

\[ -4 x y'(x)^2+4 y(x) y'(x)+x y(x) y''(x)=0 \] Mathematica : cpu = 0.134145 (sec), leaf count = 21

\[\left \{\left \{y(x)\to \frac {c_2 x}{\sqrt [3]{1+c_1 x^3}}\right \}\right \}\] Maple : cpu = 0.225 (sec), leaf count = 64

\[ \left \{ y \left ( x \right ) ={x{\frac {1}{\sqrt [3]{-3\,{\it \_C2}\,{x}^{3}+{\it \_C1}}}}},y \left ( x \right ) ={\frac { \left ( -1+i\sqrt {3} \right ) x}{2}{\frac {1}{\sqrt [3]{-3\,{\it \_C2}\,{x}^{3}+{\it \_C1}}}}},y \left ( x \right ) =-{\frac { \left ( 1+i\sqrt {3} \right ) x}{2}{\frac {1}{\sqrt [3]{-3\,{\it \_C2}\,{x}^{3}+{\it \_C1}}}}} \right \} \]