ODE
\[ x^3 y'''(x)+x y'(x)-y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.166554 (sec), leaf count = 22
\[\left \{\left \{y(x)\to x \left (c_3 \log ^2(x)+c_2 \log (x)+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 20
\[[y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} x \ln \left (x \right )+\textit {\_C3} x \ln \left (x \right )^{2}]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(C[1] + C[2]*Log[x] + C[3]*Log[x]^2)}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x+_C2*x*ln(x)+_C3*x*ln(x)^2]