ODE
\[ -y'''(x)+y'''''(x)-2 y''(x)+2 y'(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.136413 (sec), leaf count = 53
\[\left \{\left \{y(x)\to \frac {1}{2} e^{-x} \left (2 e^{2 x} \left (c_4 (x-1)+c_3\right )+\left (c_2-c_1\right ) \sin (x)-\left (c_1+c_2\right ) \cos (x)\right )+c_5\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C4}\,\sin \left ( x \right ) +{\it \_C5}\,\cos \left ( x \right ) \right ) {{\rm e}^{-x}}+ \left ( {\it \_C3}\,x+{\it \_C2} \right ) {{\rm e}^{x}}+{\it \_C1} \right \} \] Mathematica raw input
DSolve[2*y'[x] - 2*y''[x] - y'''[x] + y'''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[5] + (2*E^(2*x)*(C[3] + (-1 + x)*C[4]) - (C[1] + C[2])*Cos[x] + (-C[1] + C[2])*Sin[x])/(2*E^x)}}
Maple raw input
dsolve(diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)+2*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C4*sin(x)+_C5*cos(x))*exp(-x)+(_C3*x+_C2)*exp(x)+_C1