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 }\relax (t )&=-3 x_{1}\relax (t )+2 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-x_{1}\relax (t )-x_{2}\relax (t ) \end {align*}
With initial conditions \[ [x_{1}\relax (0) = 1, x_{2}\relax (0) = -2] \]
✓ Solution by Maple
Time used: 0.028 (sec). Leaf size: 37
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],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = -{\mathrm e}^{-2 t} \left (-\cos \relax (t )+5 \sin \relax (t )\right ) \] \[ x_{2}\relax (t ) = {\mathrm e}^{-2 t} \left (-3 \sin \relax (t )-2 \cos \relax (t )\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (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*}