37.1.5 problem 10.2.8 part(3)

Internal problem ID [6392]
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)
Date solved : Monday, January 27, 2025 at 01:58:47 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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)
 

\[ x \left (t \right ) = \left (t c_3 +c_2 \right ) {\mathrm e}^{-t}+c_1 \,{\mathrm e}^{5 t} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 26

DSolve[D[x[t],{t,3}]-3*D[x[t],{t,2}]-9*D[x[t],t]-5*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-t} \left (c_2 t+c_3 e^{6 t}+c_1\right ) \]