ODE No. 1121

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

✓ Mathematica : cpu = 0.227812 (sec), leaf count = 41

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

\[\left \{\left \{y(x)\to c_2 x \int _1^x\frac {e^{\frac {K[1]^2}{2}-K[1]}}{K[1]^2}dK[1]+c_1 x\right \}\right \}\]

✓ Maple : cpu = 0.049 (sec), leaf count = 23

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

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