5.38   ODE No. 1486

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

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

Mathematica: cpu = 0.168021 (sec), leaf count = 65 \[ \left \{\left \{y(x)\to \frac {1}{4} c_3 x \left (\frac {e^{2 x-2} \text {Ei}(2-4 x)}{x}-\frac {2 \text {Ei}(1-2 x)}{e}-\frac {e^{-2 x}}{x}\right )+c_1 x-c_2 e^{2 x}\right \}\right \} \]

Maple: cpu = 0.187 (sec), leaf count = 50 \[ \left \{ y \left ( x \right ) =x{\it \_C1}+{\it \_C2}\,{{\rm e}^{2\,x}}+ {\it \_C3}\, \left ( -{\frac {x{{\rm e}^{-1}}{\it Ei} \left ( 1,2\,x-1 \right ) }{2}}+{\frac {{\it Ei} \left ( 1,-2+4\,x \right ) {{\rm e}^{2\, x-2}}}{4}}+{\frac {{{\rm e}^{-2\,x}}}{4}} \right ) \right \} \]