ODE
\[ -2 y'''(x)+y''''(x)+2 y''(x)-2 y'(x)+y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00870298 (sec), leaf count = 27
\[\left \{\left \{y(x)\to e^x \left (c_4 x+c_3\right )+c_2 \sin (x)+c_1 \cos (x)\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C2}\,x+{\it \_C1} \right ) {{\rm e}^{x}}+{\it \_C3}\,\sin \left ( x \right ) +{\it \_C4}\,\cos \left ( x \right ) \right \} \] Mathematica raw input
DSolve[y[x] - 2*y'[x] + 2*y''[x] - 2*y'''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x*(C[3] + x*C[4]) + C[1]*Cos[x] + C[2]*Sin[x]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(diff(y(x),x),x),x)+2*diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*x+_C1)*exp(x)+_C3*sin(x)+_C4*cos(x)