ODE
\[ x^2 y''(x)-2 x y'(x)+2 y(x)=2 x \log (x) \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.163185 (sec), leaf count = 25
\[\left \{\left \{y(x)\to x \left (-\log ^2(x)-2 \log (x)+c_2 x-2+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.057 (sec), leaf count = 26
\[[y \left (x \right ) = x^{2} \textit {\_C2} +\textit {\_C1} x -x \left (\ln \left (x \right )^{2}+2 \ln \left (x \right )+2\right )]\] Mathematica raw input
DSolve[2*y[x] - 2*x*y'[x] + x^2*y''[x] == 2*x*Log[x],y[x],x]
Mathematica raw output
{{y[x] -> x*(-2 + C[1] + x*C[2] - 2*Log[x] - Log[x]^2)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x) = 2*x*ln(x), y(x))
Maple raw output
[y(x) = x^2*_C2+_C1*x-x*(ln(x)^2+2*ln(x)+2)]