Internal problem ID [762]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.6, Complex Eigenvalues. page 417
Problem number: 12.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-\frac {4 x_{1} \left (t \right )}{5}+2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+\frac {6 x_{2} \left (t \right )}{5} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 46
dsolve([diff(x__1(t),t)=-4/5*x__1(t)+2*x__2(t),diff(x__2(t),t)=-1*x__1(t)+6/5*x__2(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{\frac {t}{5}} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{\frac {t}{5}} \left (c_{1} \sin \left (t \right )-c_{2} \sin \left (t \right )+c_{1} \cos \left (t \right )+c_{2} \cos \left (t \right )\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 56
DSolve[{x1'[t]==-4/5*x1[t]+2*x2[t],x2'[t]==-1*x1[t]+6/5*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{t/5} (c_1 \cos (t)-(c_1-2 c_2) \sin (t)) \\ \text {x2}(t)\to e^{t/5} (c_2 (\sin (t)+\cos (t))-c_1 \sin (t)) \\ \end{align*}