Internal problem ID [14034]
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 (h).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=8 x \left (t \right )+2 y \left (t \right )+7 \,{\mathrm e}^{2 t}\\ y^{\prime }\left (t \right )&=4 x \left (t \right )+y \left (t \right )-7 \,{\mathrm e}^{2 t} \end {align*}
With initial conditions \[ [x \left (0\right ) = -1, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 24
dsolve([diff(x(t),t) = 8*x(t)+2*y(t)+7*exp(2*t), diff(y(t),t) = 4*x(t)+y(t)-7*exp(2*t), x(0) = -1, y(0) = 1], singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {3}{2}+\frac {{\mathrm e}^{2 t}}{2} \\ y \left (t \right ) &= 6-5 \,{\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 28
DSolve[{x'[t]==8*x[t]+2*y[t]+7*Exp[2*t],y'[t]==4*x[t]+y[t]-7*Exp[2*t]},{x[0]==-1,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} \left (e^{2 t}-3\right ) \\ y(t)\to 6-5 e^{2 t} \\ \end{align*}