Internal problem ID [752]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.6, Complex Eigenvalues. page 417
Problem number: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-x_{1} \relax (t )-4 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=x_{1} \relax (t )-x_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 46
dsolve([diff(x__1(t),t)=-1*x__1(t)-4*x__2(t),diff(x__2(t),t)=1*x__1(t)-1*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = -2 \,{\mathrm e}^{-t} \left (c_{2} \sin \left (2 t \right )-\cos \left (2 t \right ) c_{1}\right ) \] \[ x_{2} \relax (t ) = {\mathrm e}^{-t} \left (c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 55
DSolve[{x1'[t]==-1*x1[t]-4*x2[t],x2'[t]==1*x1[t]-1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-t} (c_1 \cos (2 t)-2 c_2 \sin (2 t)) \\ \text {x2}(t)\to \frac {1}{2} e^{-t} (2 c_2 \cos (2 t)+c_1 \sin (2 t)) \\ \end{align*}