Internal problem ID [760]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.6, Complex Eigenvalues. page 417
Problem number: 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-x_{2} \left (t \right ) \end {align*}
With initial conditions \[ [x_{1} \left (0\right ) = 1, x_{2} \left (0\right ) = -2] \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve([diff(x__1(t),t) = -3*x__1(t)+2*x__2(t), diff(x__2(t),t) = -x__1(t)-x__2(t), x__1(0) = 1, x__2(0) = -2], singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-2 t} \left (-5 \sin \left (t \right )+\cos \left (t \right )\right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{-2 t} \left (-6 \sin \left (t \right )-4 \cos \left (t \right )\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 27
DSolve[{x1'[t]==-3*x1[t]+2*x2[t],x2'[t]==-1*x1[t]-1*x2[t]},{x1[0]==1,x2[0]==1},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-2 t} (\sin (t)+\cos (t)) \\ \text {x2}(t)\to e^{-2 t} \cos (t) \\ \end{align*}