\[ a^4 \lambda y(x)+a^2 (\lambda +1) y''(x)+y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.0042043 (sec), leaf count = 44
DSolve[a^4*lambda*y[x] + a^2*(1 + lambda)*Derivative[2][y][x] + Derivative[4][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \cos \left (a \sqrt {\lambda } x\right )+c_2 \sin \left (a \sqrt {\lambda } x\right )+c_3 \cos (a x)+c_4 \sin (a x)\right \}\right \}\] ✓ Maple : cpu = 0.023 (sec), leaf count = 35
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+(lambda+1)*a^2*diff(diff(y(x),x),x)+lambda*a^4*y(x)=0,y(x))
\[y \left (x \right ) = \sin \left (a x \right ) c_{1}+c_{2} \cos \left (a x \right )+c_{3} \sin \left (a \sqrt {\lambda }\, x \right )+c_{4} \cos \left (a \sqrt {\lambda }\, x \right )\]