ODE
\[ 2 y'''(x)+y''''''(x)+y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00993461 (sec), leaf count = 70
\[\left \{\left \{y(x)\to e^{-x} \left (c_6 x+e^{3 x/2} \left (c_4 x+c_3\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )+e^{3 x/2} \left (c_2 x+c_1\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+c_5\right )\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 49
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {x}{2}}}} \left ( {\it \_C6}\,x+{\it \_C4} \right ) \cos \left ( {\frac {\sqrt {3}x}{2}} \right ) +{{\rm e}^{{\frac {x}{2}}}} \left ( {\it \_C5}\,x+{\it \_C3} \right ) \sin \left ( {\frac {\sqrt {3}x}{2}} \right ) +{{\rm e}^{-x}} \left ( {\it \_C2}\,x+{\it \_C1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = exp(1/2*x)*(_C6*x+_C4)*cos(1/2*3^(1/2)*x)+exp(1/2*x)*(_C5*x+_C3)*sin(1/2*3^(1/2)*x)+exp(-x)*(_C2*x+_C1)