ODE
\[ x^2 y''(x)-x y'(x)+2 y(x)=x \log (x) \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.179571 (sec), leaf count = 22
\[\{\{y(x)\to x (\log (x)+c_2 \cos (\log (x))+c_1 \sin (\log (x)))\}\}\]
Maple ✓
cpu = 0.377 (sec), leaf count = 21
\[[y \left (x \right ) = x \sin \left (\ln \left (x \right )\right ) \textit {\_C2} +x \cos \left (\ln \left (x \right )\right ) \textit {\_C1} +x \ln \left (x \right )]\] Mathematica raw input
DSolve[2*y[x] - x*y'[x] + x^2*y''[x] == x*Log[x],y[x],x]
Mathematica raw output
{{y[x] -> x*(C[2]*Cos[Log[x]] + Log[x] + C[1]*Sin[Log[x]])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+2*y(x) = x*ln(x), y(x))
Maple raw output
[y(x) = x*sin(ln(x))*_C2+x*cos(ln(x))*_C1+x*ln(x)]