ODE
\[ y''''(x)+a^4 y(x)+2 a^2 y''(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.148178 (sec), leaf count = 30
\[\{\{y(x)\to (c_2 x+c_1) \cos (a x)+(c_4 x+c_3) \sin (a x)\}\}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 31
\[[y \left (x \right ) = \textit {\_C1} \sin \left (a x \right )+\textit {\_C2} \cos \left (a x \right )+\textit {\_C3} \sin \left (a x \right ) x +\textit {\_C4} \cos \left (a x \right ) x]\] Mathematica raw input
DSolve[a^4*y[x] + 2*a^2*y''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x*C[2])*Cos[a*x] + (C[3] + x*C[4])*Sin[a*x]}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+2*a^2*diff(diff(y(x),x),x)+a^4*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*sin(a*x)+_C2*cos(a*x)+_C3*sin(a*x)*x+_C4*cos(a*x)*x]