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 = 0.00831964 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \left (c_4 x+c_3\right ) \sin (a x)+\left (c_2 x+c_1\right ) \cos (a x)\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C4}\,x+{\it \_C2} \right ) \cos \left ( ax \right ) +\sin \left ( ax \right ) \left ( {\it \_C3}\,x+{\it \_C1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = (_C4*x+_C2)*cos(a*x)+sin(a*x)*(_C3*x+_C1)