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 = 0.0150336 (sec), leaf count = 25
\[\left \{\left \{y(x)\to x \left (c_2 x+c_1-\log ^2(x)-2 \log (x)-2\right )\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) =x \left ( {\it \_C2}\,x- \left ( \ln \left ( x \right ) \right ) ^{2}+{\it \_C1}-2\,\ln \left ( x \right ) -2 \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = x*(_C2*x-ln(x)^2+_C1-2*ln(x)-2)