ODE
\[ x^3 y'''(x)+x y'(x)-y(x)=x \log (x) \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.163852 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {1}{24} x \log ^4(x)+c_1 x+c_3 x \log ^2(x)+c_2 x \log (x)\right \}\right \}\]
Maple ✓
cpu = 0.059 (sec), leaf count = 27
\[\left [y \left (x \right ) = \frac {\ln \left (x \right )^{4} x}{24}+\textit {\_C1} x +\textit {\_C2} x \ln \left (x \right )+\textit {\_C3} x \ln \left (x \right )^{2}\right ]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + x^3*y'''[x] == x*Log[x],y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + x*C[2]*Log[x] + x*C[3]*Log[x]^2 + (x*Log[x]^4)/24}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+x*diff(y(x),x)-y(x) = x*ln(x), y(x))
Maple raw output
[y(x) = 1/24*ln(x)^4*x+_C1*x+_C2*x*ln(x)+_C3*x*ln(x)^2]