8.81   ODE No. 1671

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

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

Mathematica: cpu = 0.042505 (sec), leaf count = 59 \[ \left \{\left \{y(x)\to c_2-2 i e^{c_1} \sqrt {e^{2 c_1}-x}\right \},\left \{y(x)\to c_2+2 i e^{c_1} \sqrt {e^{2 c_1}-x}\right \}\right \} \]

Maple: cpu = 0.063 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) =-2\,{\frac {\sqrt {{\it \_C1}\,x-1}}{{ \it \_C1}}}+{\it \_C2},y \left ( x \right ) =2\,{\frac {\sqrt {{\it \_C1 }\,x-1}}{{\it \_C1}}}+{\it \_C2} \right \} \]