10.16.6 problem 6

Internal problem ID [1406]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 7.6, Complex Eigenvalues. page 417
Problem number : 6
Date solved : Monday, January 27, 2025 at 04:56:51 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 49

dsolve([diff(x__1(t),t)=1*x__1(t)+2*x__2(t),diff(x__2(t),t)=-5*x__1(t)-1*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 {\sin \left (3 t \right ) c_1}{2}-\frac {\cos \left (3 t \right ) c_2}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 54

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

\begin{align*} \text {x1}(t)\to c_1 \cos (3 t)+\frac {1}{3} (c_1+2 c_2) \sin (3 t) \\ \text {x2}(t)\to c_2 \cos (3 t)-\frac {1}{3} (5 c_1+c_2) \sin (3 t) \\ \end{align*}