65.6.9 problem 12.1 (ix)

Internal problem ID [13758]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number : 12.1 (ix)
Date solved : Tuesday, January 28, 2025 at 06:02:06 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 (0\right )&=0\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 13

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

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