2.1242   ODE No. 1242

\[ \left (x^2-1\right ) y''(x)+\left (x-x^2\right ) y(x)-(3 x+1) y'(x)=0 \] Mathematica : cpu = 0.192991 (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 = 0.058 (sec), leaf count = 41


\[y \relax (x ) = c_{2} {\mathrm e}^{-2-x} \left (1+x \right )^{2} \Ei \left (1, -2 x -2\right )+c_{1} {\mathrm e}^{-x} \left (1+x \right )^{2}+2 c_{2} {\mathrm e}^{x}\]