ODE
\[ y''''(x)+2 y''(x)+y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.154008 (sec), leaf count = 26
\[\{\{y(x)\to (c_2 x+c_1) \cos (x)+(c_4 x+c_3) \sin (x)\}\}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 23
\[[y \left (x \right ) = \sin \left (x \right ) \textit {\_C1} +\textit {\_C2} \cos \left (x \right )+\textit {\_C3} \sin \left (x \right ) x +\textit {\_C4} \cos \left (x \right ) x]\] Mathematica raw input
DSolve[y[x] + 2*y''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x*C[2])*Cos[x] + (C[3] + x*C[4])*Sin[x]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+2*diff(diff(y(x),x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = sin(x)*_C1+_C2*cos(x)+_C3*sin(x)*x+_C4*cos(x)*x]