73.27.14 problem 38.10 (h)

Internal problem ID [15770]
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)
Date solved : Tuesday, January 28, 2025 at 08:06:54 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 )+7 \,{\mathrm e}^{2 t}\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )+y \left (t \right )-7 \,{\mathrm e}^{2 t} \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = -1\\ y \left (0\right ) = 1 \end{align*}

✓ Solution by Maple

Time used: 0.076 (sec). Leaf size: 23

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: 0.065 (sec). Leaf size: 28

DSolve[{D[x[t],t]==8*x[t]+2*y[t]+7*Exp[2*t],D[y[t],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*}