9.9   ODE No. 1845

\[ \boxed { 9\, \left ( y \left ( x \right ) \right ) ^{2}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -45\,y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +40\, \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{3}=0} \]

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

Mathematica: cpu = 0.074009 (sec), leaf count = 37 \[ \text {DSolve}\left [9 y(x)^2 y^{(3)}(x)+40 y'(x)^3-45 y(x) y'(x) y''(x)=0,y(x),x\right ] \]

Maple: cpu = 0.187 (sec), leaf count = 22 \[ \left \{ y \left ( x \right ) ={{\it \_C3} \left ( {{\it \_C2}}^{2}+2\,{ \it \_C2}\,x+{x}^{2}-9\,{\it \_C1} \right ) ^{-{\frac {3}{2}}}} \right \} \]