2.1194   ODE No. 1194

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

\[ x^2 y''(x)+(x+1) x y'(x)+(3 x-1) y(x)=0 \] Mathematica : cpu = 0.107314 (sec), leaf count = 65

\[\left \{\left \{y(x)\to c_1 e^{-x} (x-3) x-\frac {c_2 e^{-x} \left (x^3 (-\text {Ei}(x))+3 x^2 \text {Ei}(x)+e^x x^2-2 e^x x-e^x\right )}{6 x}\right \}\right \}\] Maple : cpu = 0.067 (sec), leaf count = 48

\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}{\it \_C2}\,{{\rm e}^{-x}} \left ( x-3 \right ) {\it Ei} \left ( 1,-x \right ) +{\it \_C1}\,{x}^{2} \left ( x-3 \right ) {{\rm e}^{-x}}+{\it \_C2}\, \left ( {x}^{2}-2\,x-1 \right ) }{x}} \right \} \]