64.24.8 problem 8

Internal problem ID [13693]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 13, Nonlinear differential equations. Section 13.2, Exercises page 656
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 05:55:21 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )+7 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right )+5 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 34

dsolve([diff(x(t),t)=x(t)+7*y(t),diff(y(t),t)=3*x(t)+5*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{8 t}+{\mathrm e}^{-2 t} c_{2} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{8 t}-\frac {3 \,{\mathrm e}^{-2 t} c_{2}}{7} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 74

DSolve[{D[x[t],t]==x[t]+7*y[t],D[y[t],t]==3*x[t]+5*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{10} e^{-2 t} \left (c_1 \left (3 e^{10 t}+7\right )+7 c_2 \left (e^{10 t}-1\right )\right ) \\ y(t)\to \frac {1}{10} e^{-2 t} \left (3 c_1 \left (e^{10 t}-1\right )+c_2 \left (7 e^{10 t}+3\right )\right ) \\ \end{align*}