2.1194   ODE No. 1194

\[ x^2 y''(x)+(x+1) x y'(x)+(3 x-1) y(x)=0 \] Mathematica : cpu = 0.0891578 (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 = 0.042 (sec), leaf count = 48


\[y \relax (x ) = \frac {x^{2} c_{2} {\mathrm e}^{-x} \left (x -3\right ) \Ei \left (1, -x \right )+c_{1} x^{2} \left (x -3\right ) {\mathrm e}^{-x}+c_{2} \left (x^{2}-2 x -1\right )}{x}\]