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 = 0.0699656 (sec), leaf count = 21
\[\left \{\left \{y(x)\to c_1 x-c_2 \sin (x)+c_3 \cos (x)\right \}\right \}\]
Maple ✓
cpu = 0.093 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,x+\cos \left ( x \right ) {\it \_C2}+{\it \_C3}\,\sin \left ( x \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*x+cos(x)*_C2+_C3*sin(x)