ODE
\[ x^2 y''(x)-2 x y'(x)+2 y(x)=x^5 \log (x) \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.015462 (sec), leaf count = 32
\[\left \{\left \{y(x)\to c_2 x^2+c_1 x-\frac {7 x^5}{144}+\frac {1}{12} x^5 \log (x)\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{5}\ln \left ( x \right ) }{12}}-{\frac {7\,{x}^{5}}{144}}+{x}^{2}{\it \_C2}+{\it \_C1}\,x \right \} \] Mathematica raw input
DSolve[2*y[x] - 2*x*y'[x] + x^2*y''[x] == x^5*Log[x],y[x],x]
Mathematica raw output
{{y[x] -> (-7*x^5)/144 + x*C[1] + x^2*C[2] + (x^5*Log[x])/12}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x) = x^5*ln(x), y(x),'implicit')
Maple raw output
y(x) = 1/12*x^5*ln(x)-7/144*x^5+x^2*_C2+_C1*x