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 }\relax (t )&=-\frac {4 x_{1}\relax (t )}{5}+2 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-x_{1}\relax (t )+\frac {6 x_{2}\relax (t )}{5} \end {align*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 48
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)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = -{\mathrm e}^{\frac {t}{5}} \left (\cos \relax (t ) c_{1}-c_{2} \cos \relax (t )-c_{1} \sin \relax (t )-\sin \relax (t ) c_{2}\right ) \] \[ x_{2}\relax (t ) = {\mathrm e}^{\frac {t}{5}} \left (c_{1} \sin \relax (t )+c_{2} \cos \relax (t )\right ) \]
✓ 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*}