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 = 0.224614 (sec), leaf count = 21
\[\{\{y(x)\to c_1 x+c_3 \cos (x)-c_2 \sin (x)\}\}\]
Maple ✓
cpu = 0.14 (sec), leaf count = 16
\[[y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} \cos \left (x \right )+\textit {\_C3} \sin \left (x \right )]\] 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[3]*Cos[x] - C[2]*Sin[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*cos(x)+_C3*sin(x)]