52.10.6 problem 6

Internal problem ID [8400]
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 : 6
Date solved : Monday, January 27, 2025 at 03:57:33 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=-6 x \left (t \right )+2 y\\ y^{\prime }&=-3 x \left (t \right )+y \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 26

dsolve([diff(x(t),t)=-6*x(t)+2*y(t),diff(y(t),t)=-3*x(t)+y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{-5 t} \\ y &= \frac {c_{2} {\mathrm e}^{-5 t}}{2}+3 c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 73

DSolve[{D[x[t],t]==-6*x[t]+2*y[t],D[y[t],t]==-3*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{5} e^{-5 t} \left (2 c_2 \left (e^{5 t}-1\right )-c_1 \left (e^{5 t}-6\right )\right ) \\ y(t)\to \frac {1}{5} e^{-5 t} \left (c_2 \left (6 e^{5 t}-1\right )-3 c_1 \left (e^{5 t}-1\right )\right ) \\ \end{align*}