2.1323   ODE No. 1323

\[ y''(x)=\frac {2 (x+1) y(x)}{(x-1) x}-\frac {2 (x-2) y'(x)}{(x-1) x} \]

✗ Mathematica : cpu = 0.385308 (sec), leaf count = 0

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

, DifferentialRoot result

\[\left \{\left \{y(x)\to (x)\right \}\right \}\]

✓ Maple : cpu = 0.026 (sec), leaf count = 17

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

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