14.7.9 problem 9

Internal problem ID [2553]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2. Linear equations with constant coefficients. Excercises page 140
Problem number : 9
Date solved : Monday, January 27, 2025 at 06:00:12 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 23

dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=0,y(0) = 1, D(y)(0) = v],y(t), singsol=all)
 

\[ y = \left (3+v \right ) {\mathrm e}^{-2 t}+\left (-v -2\right ) {\mathrm e}^{-3 t} \]

✓ Solution by Mathematica

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

DSolve[{D[y[t],{t,2}]+5*D[y[t],t]+6*y[t]==0,{y[0]==1,Derivative[1][y][0] ==v}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (e^t (v+3)-v-2\right ) \]