Internal problem ID [4541]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.2, ODEs with constant Coefficients. page
307
Problem number: 10.2.8 part(3).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 24
dsolve(diff(x(t),t$3)-3*diff(x(t),t$2)-9*diff(x(t),t)-5*x(t)=0,x(t), singsol=all)
\[ x \relax (t ) = c_{1} {\mathrm e}^{5 t}+c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{-t} t \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 26
DSolve[x'''[t]-3*x''[t]-9*x'[t]-5*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-t} \left (c_2 t+c_3 e^{6 t}+c_1\right ) \\ \end{align*}