10.9.13 problem 13

Internal problem ID [1315]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page 172
Problem number : 13
Date solved : Monday, January 27, 2025 at 04:50:49 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+82 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 23

dsolve([9*diff(y(t),t$2)+6*diff(y(t),t)+82*y(t) = 0,y(0) = -1, D(y)(0) = 2],y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-\frac {t}{3}} \left (5 \sin \left (3 t \right )-9 \cos \left (3 t \right )\right )}{9} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 29

DSolve[{9*D[y[t],{t,2}]+6*D[y[t],t]+82*y[t]==0,{y[0]==-1,Derivative[1][y][0] ==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{9} e^{-t/3} (5 \sin (3 t)-9 \cos (3 t)) \]