2.1242   ODE No. 1242

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

\[ \left (x^2-1\right ) y''(x)-\left (x^2-x\right ) y(x)-(3 x+1) y'(x)=0 \] Mathematica : cpu = 0.221168 (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 = 0.082 (sec), leaf count = 41

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