ODE
\[ x y'''(x)-y''(x)-x y'(x)+y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.211517 (sec), leaf count = 24
\[\{\{y(x)\to c_1 x-c_2 \cosh (x)+i c_3 \sinh (x)\}\}\]
Maple ✓
cpu = 0.112 (sec), leaf count = 18
\[[y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} \,{\mathrm e}^{x}+\textit {\_C3} \,{\mathrm e}^{-x}]\] Mathematica raw input
DSolve[y[x] - x*y'[x] - y''[x] + x*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] - C[2]*Cosh[x] + I*C[3]*Sinh[x]}}
Maple raw input
dsolve(x*diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x+_C2*exp(x)+_C3*exp(-x)]