64.17.2 problem 2

Internal problem ID [13622]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 7, Systems of linear differential equations. Section 7.3. Exercises page 299
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 05:54:01 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=5 x \left (t \right )+3 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )+y \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 0\\ y \left (0\right ) = 8 \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 33

dsolve([diff(x(t),t) = 5*x(t)+3*y(t), diff(y(t),t) = 4*x(t)+y(t), x(0) = 0, y(0) = 8], singsol=all)
 

\begin{align*} x \left (t \right ) &= 3 \,{\mathrm e}^{7 t}-3 \,{\mathrm e}^{-t} \\ y \left (t \right ) &= 2 \,{\mathrm e}^{7 t}+6 \,{\mathrm e}^{-t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 36

DSolve[{D[x[t],t]==5*x[t]+3*y[t],D[y[t],t]==4*x[t]+y[t]},{x[0]==0,y[0]==8},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 3 e^{-t} \left (e^{8 t}-1\right ) \\ y(t)\to 2 e^{-t} \left (e^{8 t}+3\right ) \\ \end{align*}