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 = 0.167178 (sec), leaf count = 32
\[\left \{\left \{y(x)\to -\frac {7 x^5}{144}+\frac {1}{12} x^5 \log (x)+c_2 x^2+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.062 (sec), leaf count = 24
\[\left [y \left (x \right ) = x^{2} \textit {\_C2} +\textit {\_C1} x +\frac {x^{5} \left (12 \ln \left (x \right )-7\right )}{144}\right ]\] 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))
Maple raw output
[y(x) = x^2*_C2+_C1*x+1/144*x^5*(12*ln(x)-7)]