\[ \boxed { {\it d4y} \left ( x \right ) + \left ( \lambda +1 \right ) {a}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +\lambda \,{a}^{4}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.007001 (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 = 0.015 (sec), leaf count = 35 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( ax \right ) +{\it \_C2}\,\cos \left ( ax \right ) +{\it \_C3}\,\sin \left ( a\sqrt {\lambda }x \right ) +{\it \_C4}\,\cos \left ( a\sqrt {\lambda }x \right ) \right \} \]