63.21.2 problem 1(b)

Internal problem ID [13230]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 225
Problem number : 1(b)
Date solved : Tuesday, January 28, 2025 at 05:12:45 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=x-y \left (t \right )\\ y^{\prime }\left (t \right )&=x+3 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 29

dsolve([diff(x(t),t)=x(t)-y(t),diff(y(t),t)=x(t)+3*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{2} t +c_{1} \right ) \\ y &= -{\mathrm e}^{2 t} \left (c_{2} t +c_{1} +c_{2} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 42

DSolve[{D[x[t],t]==x[t]-y[t],D[y[t],t]==x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -e^{2 t} (c_1 (t-1)+c_2 t) \\ y(t)\to e^{2 t} ((c_1+c_2) t+c_2) \\ \end{align*}