ODE
\[ 2 y'''(x)+y''''(x)+3 y''(x)+2 y'(x)+y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0103851 (sec), leaf count = 52
\[\left \{\left \{y(x)\to e^{-x/2} \left (\left (c_2 x+c_1\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )+\left (c_4 x+c_3\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 36
\[ \left \{ y \left ( x \right ) = \left ( \left ( {\it \_C4}\,x+{\it \_C2} \right ) \cos \left ( {\frac {\sqrt {3}x}{2}} \right ) +\sin \left ( {\frac {\sqrt {3}x}{2}} \right ) \left ( {\it \_C3}\,x+{\it \_C1} \right ) \right ) {{\rm e}^{-{\frac {x}{2}}}} \right \} \] Mathematica raw input
DSolve[y[x] + 2*y'[x] + 3*y''[x] + 2*y'''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((C[3] + x*C[4])*Cos[(Sqrt[3]*x)/2] + (C[1] + x*C[2])*Sin[(Sqrt[3]*x)/2])/E^(x/2)}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = ((_C4*x+_C2)*cos(1/2*3^(1/2)*x)+sin(1/2*3^(1/2)*x)*(_C3*x+_C1))*exp(-1/2*x)