7.24.14 problem 24 and 33

Internal problem ID [614]
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 : 24 and 33
Date solved : Monday, January 27, 2025 at 02:56:22 AM
CAS classification : system_of_ODEs

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) = 11\\ x_{2} \left (0\right ) = -7 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 33

dsolve([diff(x__1(t),t) = 4*x__1(t)+x__2(t), diff(x__2(t),t) = -2*x__1(t)+x__2(t), x__1(0) = 11, x__2(0) = -7], singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= -4 \,{\mathrm e}^{2 t}+15 \,{\mathrm e}^{3 t} \\ x_{2} \left (t \right ) &= 8 \,{\mathrm e}^{2 t}-15 \,{\mathrm e}^{3 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 34

DSolve[{D[x1[t],t]==4*x1[t]+x2[t],D[x2[t],t]==-2*x1[t]+x2[t]},{x1[0]==11,x2[0]==-7},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{2 t} \left (15 e^t-4\right ) \\ \text {x2}(t)\to e^{2 t} \left (8-15 e^t\right ) \\ \end{align*}