28.4.32 problem 7.32

Internal problem ID [4564]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 7. Systems of linear differential equations. Problems at page 351
Problem number : 7.32
Date solved : Monday, January 27, 2025 at 09:23:32 AM
CAS classification : system_of_ODEs

\begin{align*} x_{1}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-x_{2} \left (t \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 28

dsolve([diff(x__1(t),t) = 5*x__1(t)+3*x__2(t), diff(x__2(t),t) = -3*x__1(t)-x__2(t), x__1(0) = 1, x__2(0) = -2], singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (-3 t +1\right ) \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{2 t} \left (-9 t +6\right )}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

DSolve[{D[x1[t],t]==5*x1[t]+3*x2[t],D[x2[t],t]==-3*x1[t]-x2[t]},{x1[0]==1,x2[0]==-2},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{2 t} (1-3 t) \\ \text {x2}(t)\to e^{2 t} (3 t-2) \\ \end{align*}