ODE
\[ y''''(x)+a^2 y''(x)=0 \] ODE Classification
[[_high_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0268292 (sec), leaf count = 34
\[\left \{\left \{y(x)\to -\frac {c_2 \sin (a x)}{a^2}-\frac {c_1 \cos (a x)}{a^2}+c_4 x+c_3\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={\it \_C1}+x{\it \_C2}+{\it \_C3}\,\sin \left ( ax \right ) +{\it \_C4}\,\cos \left ( ax \right ) \right \} \] Mathematica raw input
DSolve[a^2*y''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[3] + x*C[4] - (C[1]*Cos[a*x])/a^2 - (C[2]*Sin[a*x])/a^2}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+a^2*diff(diff(y(x),x),x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1+x*_C2+_C3*sin(a*x)+_C4*cos(a*x)