13.9.5 problem 6

Internal problem ID [2391]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number : 6
Date solved : Monday, January 27, 2025 at 05:51:23 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 10

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

\[ y = {\mathrm e}^{-t +2} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 12

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

\[ y(t)\to e^{2-t} \]