35.8.4 problem 4

Internal problem ID [6211]
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
Date solved : Monday, January 27, 2025 at 01:47:48 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} r^{\prime \prime }-6 r^{\prime }+9 r&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(diff(r(t),t$2)-6*diff(r(t),t)+9*r(t)=0,r(t), singsol=all)
 

\[ r = {\mathrm e}^{3 t} \left (c_{2} t +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 18

DSolve[D[r[t],{t,2}]-6*D[r[t],t]+9*r[t]==0,r[t],t,IncludeSingularSolutions -> True]
 

\[ r(t)\to e^{3 t} (c_2 t+c_1) \]