73.27.13 problem 38.10 (g)

Internal problem ID [15769]
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 : 38.10 (g)
Date solved : Tuesday, January 28, 2025 at 08:06:53 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=8 x \left (t \right )+2 y \left (t \right )-17\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )+y \left (t \right )-13 \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 0\\ y \left (0\right ) = 0 \end{align*}

✓ Solution by Maple

Time used: 0.118 (sec). Leaf size: 27

dsolve([diff(x(t),t) = 8*x(t)+2*y(t)-17, diff(y(t),t) = 4*x(t)+y(t)-13, x(0) = 0, y(0) = 0], singsol=all)
 

\begin{align*} x \left (t \right ) &= -2 \,{\mathrm e}^{9 t}+t +2 \\ y \left (t \right ) &= -{\mathrm e}^{9 t}+1-4 t \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 30

DSolve[{D[x[t],t]==8*x[t]+2*y[t]-17,D[y[t],t]==4*x[t]+y[t]-13},{x[0]==0,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to t-2 e^{9 t}+2 \\ y(t)\to -4 t-e^{9 t}+1 \\ \end{align*}