Internal problem ID [9115]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1536.
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 }+\lambda y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 50
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+lambda*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-i \left (-\lambda \right )^{\frac {1}{4}} x}+c_{2} {\mathrm e}^{i \left (-\lambda \right )^{\frac {1}{4}} x}+c_{3} {\mathrm e}^{-\left (-\lambda \right )^{\frac {1}{4}} x}+c_{4} {\mathrm e}^{\left (-\lambda \right )^{\frac {1}{4}} x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 76
DSolve[\[Lambda]*y[x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{(-1)^{3/4} \sqrt [4]{\lambda } x}+c_2 e^{-\sqrt [4]{-1} \sqrt [4]{\lambda } x}+c_3 e^{-(-1)^{3/4} \sqrt [4]{\lambda } x}+c_4 e^{\sqrt [4]{-1} \sqrt [4]{\lambda } x} \\ \end{align*}