14.22.1 problem 1

Internal problem ID [2728]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Section 3.8, Systems of differential equations. The eigenva1ue-eigenvector method. Page 339
Problem number : 1
Date solved : Monday, January 27, 2025 at 06:12:24 AM
CAS classification : system_of_ODEs

\begin{align*} x_{1}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )-3 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 34

dsolve([diff(x__1(t),t)=6*x__1(t)-3*x__2(t),diff(x__2(t),t)=2*x__1(t)+1*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= c_1 \,{\mathrm e}^{4 t}+c_2 \,{\mathrm e}^{3 t} \\ x_{2} \left (t \right ) &= \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[ x1[t],t]==6*x1[t]-3*x2[t],D[ x2[t],t]==2*x1[t]+1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{3 t} \left (c_1 \left (3 e^t-2\right )-3 c_2 \left (e^t-1\right )\right ) \\ \text {x2}(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*}