ODE No. 1112

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

✓ Mathematica : cpu = 0.0148125 (sec), leaf count = 30

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

\[\left \{\left \{y(x)\to c_1 e^{2 x}-\frac {1}{9} c_2 e^{-x} (3 x+1)\right \}\right \}\]

✓ Maple : cpu = 0.036 (sec), leaf count = 22

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

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