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 = 0.0214698 (sec), leaf count = 22
\[\left \{\left \{y(x)\to x \left (c_1 \sin (\log (x))+c_2 \cos (\log (x))+\log (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) =x \left ( \sin \left ( \ln \left ( x \right ) \right ) {\it \_C2}+\cos \left ( \ln \left ( x \right ) \right ) {\it \_C1}+\ln \left ( x \right ) \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = x*(sin(ln(x))*_C2+cos(ln(x))*_C1+ln(x))