64.18.3 problem 23

Internal problem ID [13626]
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 : 23
Date solved : Tuesday, January 28, 2025 at 05:54:04 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-2 x \left (t \right )+7 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right )+2 y \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 9\\ y \left (0\right ) = -1 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 33

dsolve([diff(x(t),t) = -2*x(t)+7*y(t), diff(y(t),t) = 3*x(t)+2*y(t), x(0) = 9, y(0) = -1], singsol=all)
 

\begin{align*} x \left (t \right ) &= 2 \,{\mathrm e}^{5 t}+7 \,{\mathrm e}^{-5 t} \\ y \left (t \right ) &= 2 \,{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-5 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 38

DSolve[{D[x[t],t]==-2*x[t]+7*y[t],D[y[t],t]==3*x[t]+2*y[t]},{x[0]==9,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 7 e^{-5 t}+2 e^{5 t} \\ y(t)\to 2 e^{5 t}-3 e^{-5 t} \\ \end{align*}