73.27.19 problem 38.11

Internal problem ID [15775]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 38. Systems of differential equations. A starting point. Additional Exercises. page 786
Problem number : 38.11
Date solved : Tuesday, January 28, 2025 at 08:06:59 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=5 x \left (t \right )+4 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=8 x \left (t \right )+y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 34

dsolve([diff(x(t),t)=5*x(t)+4*y(t),diff(y(t),t)=8*x(t)+y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{-3 t} c_{1} +c_{2} {\mathrm e}^{9 t} \\ y \left (t \right ) &= -2 \,{\mathrm e}^{-3 t} c_{1} +c_{2} {\mathrm e}^{9 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 71

DSolve[{D[x[t],t]==5*x[t]+4*y[t],D[y[t],t]==8*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{3} e^{-3 t} \left (c_1 \left (2 e^{12 t}+1\right )+c_2 \left (e^{12 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-3 t} \left (2 c_1 \left (e^{12 t}-1\right )+c_2 \left (e^{12 t}+2\right )\right ) \\ \end{align*}