ODE
\[ y''''(x)+2 y''(x)+y(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00805373 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \left (c_4 x+c_3\right ) \sin (x)+\left (c_2 x+c_1\right ) \cos (x)\right \}\right \}\]
Maple ✓
cpu = 0.004 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C4}\,x+{\it \_C2} \right ) \cos \left ( x \right ) +\sin \left ( x \right ) \left ( {\it \_C3}\,x+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[y[x] + 2*y''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[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),'implicit')
Maple raw output
y(x) = (_C4*x+_C2)*cos(x)+sin(x)*(_C3*x+_C1)