20.20.10 problem 10

Internal problem ID [3900]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 9, First order linear systems. Section 9.11 (Chapter review), page 665
Problem number : 10
Date solved : Monday, January 27, 2025 at 08:04:14 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )-10 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=5 x_{1} \left (t \right )+11 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 47

dsolve([diff(x__1(t),t)=-3*x__1(t)-10*x__2(t),diff(x__2(t),t)=5*x__1(t)+11*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{4 t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{4 t} \left (7 c_{1} \sin \left (t \right )-\sin \left (t \right ) c_{2} +\cos \left (t \right ) c_{1} +7 c_{2} \cos \left (t \right )\right )}{10} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 57

DSolve[{D[x1[t],t]==-3*x1[t]-10*x2[t],D[x2[t],t]==5*x1[t]+11*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{4 t} (c_1 \cos (t)-(7 c_1+10 c_2) \sin (t)) \\ \text {x2}(t)\to e^{4 t} (c_2 \cos (t)+(5 c_1+7 c_2) \sin (t)) \\ \end{align*}