Internal problem ID [4359]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page
466
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {r^{\prime \prime }-6 r^{\prime }+9 r=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(r(t),t$2)-6*diff(r(t),t)+9*r(t)=0,r(t), singsol=all)
\[ r \relax (t ) = c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{3 t} t \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 18
DSolve[r''[t]-6*r'[t]+9*r[t]==0,r[t],t,IncludeSingularSolutions -> True]
\begin{align*} r(t)\to e^{3 t} (c_2 t+c_1) \\ \end{align*}