ODE No. 1251

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

✓ Mathematica : cpu = 0.0230958 (sec), leaf count = 25

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

\[\{\{y(x)\to c_1 (x-1)+c_2 (x \log (x)-\log (x)-4)\}\}\]

✓ Maple : cpu = 0.036 (sec), leaf count = 20

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

\[y \left (x \right ) = c_{2} \left (x -1\right ) \ln \left (x \right )-4 c_{2} +c_{1} \left (x -1\right )\]