7.24.12 problem 22 and 31

Internal problem ID [612]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 5. Linear systems of differential equations. Section 5.3 (Matrices and linear systems). Problems at page 364
Problem number : 22 and 31
Date solved : Monday, January 27, 2025 at 02:56:21 AM
CAS classification : system_of_ODEs

\begin{align*} x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) = 0\\ x_{2} \left (0\right ) = 5 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 33

dsolve([diff(x__1(t),t) = -3*x__1(t)+2*x__2(t), diff(x__2(t),t) = -3*x__1(t)+4*x__2(t), x__1(0) = 0, x__2(0) = 5], singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 37

DSolve[{D[x1[t],t]==-3*x1[t]+2*x2[t],D[x2[t],t]==-3*x1[t]+4*x2[t]},{x1[0]==0,x2[0]==5},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to 2 e^{-2 t} \left (e^{5 t}-1\right ) \\ \text {x2}(t)\to e^{-2 t} \left (6 e^{5 t}-1\right ) \\ \end{align*}