52.10.20 problem 21

Internal problem ID [8414]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. EXERCISES 8.2. Page 346
Problem number : 21
Date solved : Monday, January 27, 2025 at 04:00:13 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=-x \left (t \right )+3 y\\ y^{\prime }&=-3 x \left (t \right )+5 y \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 32

dsolve([diff(x(t),t)=-x(t)+3*y(t),diff(y(t),t)=-3*x(t)+5*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{2} t +c_{1} \right ) \\ y &= \frac {{\mathrm e}^{2 t} \left (3 c_{2} t +3 c_{1} +c_{2} \right )}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 46

DSolve[{D[x[t],t]==-x[t]+3*y[t],D[y[t],t]==-3*x[t]+5*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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