52.10.18 problem 19

Internal problem ID [8412]
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 : 19
Date solved : Monday, January 27, 2025 at 04:00:11 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=3 x \left (t \right )-y\\ y^{\prime }&=9 x \left (t \right )-3 y \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 23

dsolve([diff(x(t),t)=3*x(t)-y(t),diff(y(t),t)=9*x(t)-3*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 34

DSolve[{D[x[t],t]==3*x[t]-y[t],D[y[t],t]==9*x[t]-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 3 c_1 t-c_2 t+c_1 \\ y(t)\to 9 c_1 t-3 c_2 t+c_2 \\ \end{align*}