Internal problem ID [5225]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 74
Problem number: 4(h).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-3 y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(diff(y(x),x$3)-3*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x} c_{1}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{-x} x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 26
DSolve[y'''[x]-3*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (c_2 x+c_3 e^{3 x}+c_1\right ) \\ \end{align*}