Internal problem ID [9028]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1449.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-\lambda y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 53
dsolve(diff(diff(diff(y(x),x),x),x)-lambda*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\left (-\frac {\lambda ^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \lambda ^{\frac {1}{3}}}{2}\right ) x}+c_{2} {\mathrm e}^{\left (-\frac {\lambda ^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \lambda ^{\frac {1}{3}}}{2}\right ) x}+c_{3} {\mathrm e}^{\lambda ^{\frac {1}{3}} x} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 53
DSolve[-(\[Lambda]*y[x]) + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{(-1)^{2/3} \sqrt [3]{\lambda } x}+c_2 e^{-\sqrt [3]{-1} \sqrt [3]{\lambda } x}+c_3 e^{\sqrt [3]{\lambda } x} \\ \end{align*}