ODE
\[ x^2 y''(x)+x y'(x)+y(x)=\log (x) \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.185739 (sec), leaf count = 20
\[\{\{y(x)\to \log (x)+c_1 \cos (\log (x))+c_2 \sin (\log (x))\}\}\]
Maple ✓
cpu = 0.425 (sec), leaf count = 17
\[[y \left (x \right ) = \sin \left (\ln \left (x \right )\right ) \textit {\_C2} +\cos \left (\ln \left (x \right )\right ) \textit {\_C1} +\ln \left (x \right )]\] Mathematica raw input
DSolve[y[x] + x*y'[x] + x^2*y''[x] == Log[x],y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cos[Log[x]] + Log[x] + C[2]*Sin[Log[x]]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)+y(x) = ln(x), y(x))
Maple raw output
[y(x) = sin(ln(x))*_C2+cos(ln(x))*_C1+ln(x)]