63.22.9 problem 5

Internal problem ID [13239]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 237
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 05:12:52 AM
CAS classification : system_of_ODEs

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

With initial conditions

\begin{align*} x \left (0\right ) = 1\\ y \left (0\right ) = -1 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 13

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

\begin{align*} x \left (t \right ) &= {\mathrm e}^{t} \\ y &= -{\mathrm e}^{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 16

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

\begin{align*} x(t)\to e^t \\ y(t)\to -e^t \\ \end{align*}