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 = 0.0158627 (sec), leaf count = 33
\[\left \{\left \{y(x)\to c_1 x+c_3 x \log ^2(x)+c_2 x \log (x)+\frac {1}{24} x \log ^4(x)\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\frac {x \left ( \left ( \ln \left ( x \right ) \right ) ^{4}+24\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C3}+24\,{\it \_C2}\,\ln \left ( x \right ) +24\,{\it \_C1} \right ) }{24}} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/24*x*(ln(x)^4+24*ln(x)^2*_C3+24*_C2*ln(x)+24*_C1)