ODE No. 1307

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

DSolve[-2*y[x] + x*(1 + x)*Derivative[1][y][x] + x^3*Derivative[2][y][x] == 0,y[x],x]
 

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

dsolve(x^3*diff(diff(y(x),x),x)+x*(1+x)*diff(y(x),x)-2*y(x)=0,y(x))
 

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