\[ a^4 \lambda y(x)+a^2 (\lambda +1) y''(x)+y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.00659291 (sec), leaf count = 44
\[\left \{\left \{y(x)\to c_2 \sin \left (a \sqrt {\lambda } x\right )+c_1 \cos \left (a \sqrt {\lambda } x\right )+c_4 \sin (a x)+c_3 \cos (a x)\right \}\right \}\] ✓ Maple : cpu = 0.036 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( ax \right ) +{\it \_C2}\,\cos \left ( ax \right ) +{\it \_C3}\,\sin \left ( a\sqrt {\lambda }x \right ) +{\it \_C4}\,\cos \left ( a\sqrt {\lambda }x \right ) \right \} \]