Internal problem ID [9118]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1539.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+\left (\lambda +1\right ) a^{2} y^{\prime \prime }+\lambda \,a^{4} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 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), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (a x \right )+c_{2} \cos \left (a x \right )+c_{3} \sin \left (a \sqrt {\lambda }\, x \right )+c_{4} \cos \left (a \sqrt {\lambda }\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 44
DSolve[a^4*\[Lambda]*y[x] + a^2*(1 + \[Lambda])*y''[x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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) \\ \end{align*}