2.1196   ODE No. 1196

\[ x^2 y''(x)-(x-1) x y'(x)+(x-1) y(x)=0 \]

Mathematica : cpu = 0.0395362 (sec), leaf count = 37

DSolve[(-1 + x)*y[x] - (-1 + x)*x*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
 
\[\left \{\left \{y(x)\to \frac {c_2 \left (x^2 \text {Ei}(x)-e^x x-e^x\right )}{2 x}+c_1 x\right \}\right \}\]

Maple : cpu = 0.046 (sec), leaf count = 31

dsolve(x^2*diff(diff(y(x),x),x)-x*(x-1)*diff(y(x),x)+(x-1)*y(x)=0,y(x))
 
\[y \left (x \right ) = \frac {\operatorname {Ei}_{1}\left (-x \right ) c_{2} x^{2}+\left (1+x \right ) c_{2} {\mathrm e}^{x}+c_{1} x^{2}}{x}\]