10.16.3 problem 3

Internal problem ID [1403]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 7.6, Complex Eigenvalues. page 417
Problem number : 3
Date solved : Monday, January 27, 2025 at 04:56:48 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 37

dsolve([diff(x__1(t),t)=2*x__1(t)-5*x__2(t),diff(x__2(t),t)=1*x__1(t)-2*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= c_1 \sin \left (t \right )+c_2 \cos \left (t \right ) \\ x_{2} \left (t \right ) &= -\frac {\cos \left (t \right ) c_1}{5}+\frac {\sin \left (t \right ) c_2}{5}+\frac {2 c_1 \sin \left (t \right )}{5}+\frac {2 c_2 \cos \left (t \right )}{5} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 41

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

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