14.20.3 problem 3

Internal problem ID [2700]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.14, The method of elimination for systems. Excercises page 258
Problem number : 3
Date solved : Monday, January 27, 2025 at 06:12:00 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

dsolve([diff(x(t),t)=6*x(t)-3*y(t),diff(y(t),t)=2*x(t)+y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_1 \,{\mathrm e}^{4 t}+c_2 \,{\mathrm e}^{3 t} \\ y &= \frac {2 c_1 \,{\mathrm e}^{4 t}}{3}+c_2 \,{\mathrm e}^{3 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 60

DSolve[{D[x[t],t]==6*x[t]-3*y[t],D[y[t],t]==2*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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