\[ a^4 \lambda y(x)+a^2 (\lambda +1) y''(x)+y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.0053249 (sec), leaf count = 44
\[\left \{\left \{y(x)\to c_1 \cos \left (a \sqrt {\lambda } x\right )+c_2 \sin \left (a \sqrt {\lambda } x\right )+c_3 \cos (a x)+c_4 \sin (a x)\right \}\right \}\] ✓ Maple : cpu = 0.032 (sec), leaf count = 35
\[y \relax (x ) = c_{1} \sin \left (a x \right )+c_{2} \cos \left (a x \right )+c_{3} \sin \left (a \sqrt {\lambda }\, x \right )+c_{4} \cos \left (a \sqrt {\lambda }\, x \right )\]