9.4.10 problem problem 10

Internal problem ID [974]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 7.3, The eigenvalue method for linear systems. Page 395
Problem number : problem 10
Date solved : Wednesday, February 05, 2025 at 04:51:22 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 49

dsolve([diff(x__1(t),t)=-3*x__1(t)-2*x__2(t),diff(x__2(t),t)=9*x__1(t)+3*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= \sin \left (3 t \right ) c_1 +\cos \left (3 t \right ) c_2 \\ x_{2} \left (t \right ) &= -\frac {3 \cos \left (3 t \right ) c_1}{2}+\frac {3 \sin \left (3 t \right ) c_2}{2}-\frac {3 \sin \left (3 t \right ) c_1}{2}-\frac {3 \cos \left (3 t \right ) c_2}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 53

DSolve[{D[ x1[t],t]==-3*x1[t]-2*x2[t],D[ x2[t],t]==9*x1[t]+3*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to c_1 \cos (3 t)-\frac {1}{3} (3 c_1+2 c_2) \sin (3 t) \\ \text {x2}(t)\to c_2 \cos (3 t)+(3 c_1+c_2) \sin (3 t) \\ \end{align*}