7.23.1 problem 1

Internal problem ID [587]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 5. Linear systems of differential equations. Section 5.2 (Applications). Problems at page 345
Problem number : 1
Date solved : Monday, January 27, 2025 at 02:55:05 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=-x+3 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 26

dsolve([diff(x(t),t)=-x(t)+3*y(t),diff(y(t),t)=2*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_2 \,{\mathrm e}^{2 t}+{\mathrm e}^{-t} c_1 \\ y \left (t \right ) &= c_2 \,{\mathrm e}^{2 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 35

DSolve[{D[x[t],t]==-x[t]+3*y[t],D[y[t],t]==2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{-t} \left (c_2 \left (e^{3 t}-1\right )+c_1\right ) \\ y(t)\to c_2 e^{2 t} \\ \end{align*}