14.9.3 problem 3

Internal problem ID [2569]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2.2. Equal roots, reduction of order. Excercises page 149
Problem number : 3
Date solved : Monday, January 27, 2025 at 06:00:56 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 13

dsolve([9*diff(y(t),t$2)+6*diff(y(t),t)+y(t)=0,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-\frac {t}{3}} \left (3+t \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 19

DSolve[{9*D[y[t],{t,2}]+6*D[y[t],t]+y[t]==0,{y[0]==1,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} e^{-t/3} (t+3) \]