64.24.4 problem 4

Internal problem ID [13689]
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 : 4
Date solved : Tuesday, January 28, 2025 at 05:55:18 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )+5 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )-2 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 35

dsolve([diff(x(t),t)=2*x(t)+5*y(t),diff(y(t),t)=x(t)-2*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{-3 t} c_{1} +c_{2} {\mathrm e}^{3 t} \\ y \left (t \right ) &= -{\mathrm e}^{-3 t} c_{1} +\frac {c_{2} {\mathrm e}^{3 t}}{5} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 71

DSolve[{D[x[t],t]==2*x[t]+5*y[t],D[y[t],t]==x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{6} e^{-3 t} \left (c_1 \left (5 e^{6 t}+1\right )+5 c_2 \left (e^{6 t}-1\right )\right ) \\ y(t)\to \frac {1}{6} e^{-3 t} \left (c_1 \left (e^{6 t}-1\right )+c_2 \left (e^{6 t}+5\right )\right ) \\ \end{align*}