Internal problem ID [5049]
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]]
\[ \boxed {x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ x \left (t \right ) = \left (c_{3} t +c_{2} \right ) {\mathrm e}^{-t}+c_{1} {\mathrm e}^{5 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[x'''[t]-3*x''[t]-9*x'[t]-5*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-t} \left (c_2 t+c_3 e^{6 t}+c_1\right ) \]