4.242   ODE No. 1242

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

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

Mathematica: cpu = 0.074509 (sec), leaf count = 68 \[ \left \{\left \{y(x)\to c_1 e^{-x} (x+1)^2-c_2 e^{-x-2} \left (x^2 (-\text {Ei}(2 (x+1)))-2 x \text {Ei}(2 (x+1))-\text {Ei}(2 (x+1))+2 e^{2 x+2}\right )\right \}\right \} \]

Maple: cpu = 0.063 (sec), leaf count = 42 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-x}} \left ( 1+x \right ) ^{2}+{\it \_C2}\, \left ( {{\rm e}^{-2-x}} \left ( 1+x \right ) ^{2}{\it Ei} \left ( 1,-2\,x-2 \right ) +2\,{{\rm e}^{x}} \right ) \right \} \]