50.29.5 problem 3(a)

Internal problem ID [8201]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 10. Systems of First-Order Equations. Section A. Drill exercises. Page 400
Problem number : 3(a)
Date solved : Monday, January 27, 2025 at 03:45:45 PM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 40

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

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