4.196   ODE No. 1196

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

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

Mathematica: cpu = 0.025003 (sec), leaf count = 37 \[ \left \{\left \{y(x)\to \frac {c_2 \left (x^2 \text {Ei}(x)-e^x x-e^x\right )}{2 x}+c_1 x\right \}\right \} \]

Maple: cpu = 0.031 (sec), leaf count = 27 \[ \left \{ y \left ( x \right ) =x{\it \_C1}+{\it \_C2}\, \left ( {\frac { \left ( 1+x \right ) {{\rm e}^{x}}}{x}}+x{\it Ei} \left ( 1,-x \right ) \right ) \right \} \]