Internal problem ID [14033]
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).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=8 x \left (t \right )+2 y \left (t \right )-17\\ y^{\prime }\left (t \right )&=4 x \left (t \right )+y \left (t \right )-13 \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 28
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: 0.004 (sec). Leaf size: 30
DSolve[{x'[t]==8*x[t]+2*y[t]-17,y'[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*}