64.18.4 problem 24

Internal problem ID [13627]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 7, Systems of linear differential equations. Section 7.4. Exercises page 309
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 05:54:05 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-2 x \left (t \right )+y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=7 x \left (t \right )+4 y \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 6\\ y \left (0\right ) = 2 \end{align*}

✓ Solution by Maple

Time used: 0.045 (sec). Leaf size: 31

dsolve([diff(x(t),t) = -2*x(t)+y(t), diff(y(t),t) = 7*x(t)+4*y(t), x(0) = 6, y(0) = 2], singsol=all)
 

\begin{align*} x \left (t \right ) &= 5 \,{\mathrm e}^{-3 t}+{\mathrm e}^{5 t} \\ y \left (t \right ) &= -5 \,{\mathrm e}^{-3 t}+7 \,{\mathrm e}^{5 t} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[{D[x[t],t]==-2*x[t]+y[t],D[y[t],t]==7*x[t]+4*y[t]},{x[0]==6,y[0]==2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{-3 t} \left (e^{8 t}+5\right ) \\ y(t)\to e^{-3 t} \left (7 e^{8 t}-5\right ) \\ \end{align*}