3.540   ODE No. 540

\[ \boxed { 2\,y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{3}-y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+2\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -x=0} \]

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

Mathematica: cpu = 0.019502 (sec), leaf count = 69 \[ \left \{\left \{y(x)\to c_1+\frac {x}{2}\right \},\left \{y(x)\to \frac {\left (3 c_1-2 i x^{3/2}\right ){}^{2/3}}{2^{2/3}}\right \},\left \{y(x)\to \frac {\left (3 c_1+2 i x^{3/2}\right ){}^{2/3}}{2^{2/3}}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 109 \[ \left \{ x+{\frac {{\it \_C1}\,x}{y \left ( x \right ) } \left ( {\frac { 1}{y \left ( x \right ) } \left ( -\sqrt {-xy \left ( x \right ) }+y \left ( x \right ) \right ) } \right ) ^{-{\frac {2}{3}}} \left ( {\frac {1}{y \left ( x \right ) } \left ( -x+\sqrt {-xy \left ( x \right ) }+y \left ( x \right ) \right ) } \right ) ^{-{\frac {2}{3}}}}=0,x+{\frac {{ \it \_C1}\,x}{y \left ( x \right ) } \left ( {\frac {1}{y \left ( x \right ) } \left ( \sqrt {-xy \left ( x \right ) }+y \left ( x \right ) \right ) } \right ) ^{-{\frac {2}{3}}} \left ( {\frac {1}{y \left ( x \right ) } \left ( -x-\sqrt {-xy \left ( x \right ) }+y \left ( x \right ) \right ) } \right ) ^{-{\frac {2}{3}}}}=0,y \left ( x \right ) ={\frac {x }{2}}+{\it \_C1} \right \} \]