2.1307   ODE No. 1307

\[ x^3 y''(x)+(x+1) x y'(x)-2 y(x)=0 \] Mathematica : cpu = 0.101345 (sec), leaf count = 54


\[\left \{\left \{y(x)\to \frac {c_1 e^{\frac {1}{x}} (x+1)}{x}-\frac {c_2 \left (e^{\frac {1}{x}} x \text {Ei}\left (-\frac {1}{x}\right )+e^{\frac {1}{x}} \text {Ei}\left (-\frac {1}{x}\right )+x\right )}{x}\right \}\right \}\] Maple : cpu = 0.042 (sec), leaf count = 36


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