5.63   ODE No. 1511

\[ \boxed { {x}^{3}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +3\,{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,y \left ( x \right ) -6\,{x}^{3} \left ( x-1 \right ) \ln \left ( x \right ) +{x}^{3} \left ( x+8 \right ) =0} \]

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

Mathematica: cpu = 0.035505 (sec), leaf count = 51 \[ \left \{\left \{y(x)\to \frac {c_1}{x^2}+c_2 x+c_3 x \log (x)+\frac {1}{450} \left (-50 x^4+50 x^4 \log (x)-18 x^3-135 x^3 \log (x)\right )\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\frac {{x}^{3} \left ( 50\,x\ln \left ( x \right ) -135\,\ln \left ( x \right ) -50\,x-18 \right ) }{450}}+x{\it \_C1}+{\frac {{\it \_C2}}{{x}^{2}}}+{\it \_C3}\,x\ln \left ( x \right ) \right \} \]