ODE
\[ 2 y'''(x)+y''''''(x)+y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.162569 (sec), leaf count = 70
\[\left \{\left \{y(x)\to e^{-x} \left (c_6 x+e^{3 x/2} (c_2 x+c_1) \cos \left (\frac {\sqrt {3} x}{2}\right )+e^{3 x/2} (c_4 x+c_3) \sin \left (\frac {\sqrt {3} x}{2}\right )+c_5\right )\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 72
\[\left [y \left (x \right ) = {\mathrm e}^{-x} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{-x} x +\textit {\_C3} \,{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+\textit {\_C4} \,{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\textit {\_C5} \,{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) x +\textit {\_C6} \,{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) x\right ]\] Mathematica raw input
DSolve[y[x] + 2*y'''[x] + y''''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[5] + x*C[6] + E^((3*x)/2)*(C[1] + x*C[2])*Cos[(Sqrt[3]*x)/2] + E^((3*x)/2)*(C[3] + x*C[4])*Sin[(Sqrt[3]*x)/2])/E^x}}
Maple raw input
dsolve(diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = exp(-x)*_C1+_C2*exp(-x)*x+_C3*exp(1/2*x)*sin(1/2*3^(1/2)*x)+_C4*exp(1/2*x)*cos(1/2*3^(1/2)*x)+_C5*exp(1/2*x)*sin(1/2*3^(1/2)*x)*x+_C6*exp(1/2*x)*cos(1/2*3^(1/2)*x)*x]