7.24.11 problem 21

Internal problem ID [611]
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 : 21
Date solved : Monday, January 27, 2025 at 02:56:21 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 31

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

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} c_1 +c_2 \,{\mathrm e}^{t} \\ x_{2} \left (t \right ) &= -{\mathrm e}^{2 t} c_1 -\frac {3 c_2 \,{\mathrm e}^{t}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 56

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

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