79.2.10 problem 6 (iii)

Internal problem ID [18523]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 4. Autonomous systems. Exercises at page 69
Problem number : 6 (iii)
Date solved : Tuesday, January 28, 2025 at 11:51:54 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 12

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

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