\[ y''(x)=\frac {y'(x)}{x \log (x)}+y(x) \log ^2(x) \] ✓ Mathematica : cpu = 0.0118503 (sec), leaf count = 29
DSolve[Derivative[2][y][x] == Log[x]^2*y[x] + Derivative[1][y][x]/(x*Log[x]),y[x],x]
\[\{\{y(x)\to c_1 \cosh (x (\log (x)-1))+i c_2 \sinh (x (\log (x)-1))\}\}\] ✓ Maple : cpu = 0.01 (sec), leaf count = 23
dsolve(diff(diff(y(x),x),x) = 1/x/ln(x)*diff(y(x),x)+ln(x)^2*y(x),y(x))
\[y \left (x \right ) = c_{1} \sinh \left (x \left (\ln \left (x \right )-1\right )\right )+c_{2} \cosh \left (x \left (\ln \left (x \right )-1\right )\right )\]