52.9.11 problem 11

Internal problem ID [8389]
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 8.1. Page 332
Problem number : 11
Date solved : Monday, January 27, 2025 at 03:57:23 PM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=3 x \left (t \right )-4 y\\ y^{\prime }&=4 x \left (t \right )-7 y \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 31

dsolve([diff(x(t),t)=3*x(t)-4*y(t),diff(y(t),t)=4*x(t)-7*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[{D[x[t],t]==3*x[t]-4*y[t],D[y[t],t]==4*x[t]-7*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{3} e^{-5 t} \left (c_1 \left (4 e^{6 t}-1\right )-2 c_2 \left (e^{6 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-5 t} \left (2 c_1 \left (e^{6 t}-1\right )-c_2 \left (e^{6 t}-4\right )\right ) \\ \end{align*}