Internal problem ID [756]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.6, Complex Eigenvalues. page 417
Problem number: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-5 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
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 ) &= c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right ) \\ x_{2} \left (t \right ) &= \frac {3 c_{1} \cos \left (3 t \right )}{2}-\frac {3 c_{2} \sin \left (3 t \right )}{2}-\frac {c_{1} \sin \left (3 t \right )}{2}-\frac {c_{2} \cos \left (3 t \right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 54
DSolve[{x1'[t]==1*x1[t]+2*x2[t],x2'[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*}