ODE No. 1321

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

✓ Mathematica : cpu = 0.0187738 (sec), leaf count = 18

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

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

✓ Maple : cpu = 0.03 (sec), leaf count = 15

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

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