Internal problem ID [765]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.6, Complex Eigenvalues. page 417
Problem number: 25.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-\frac {x_{1}\relax (t )}{2}-\frac {x_{2}\relax (t )}{8}\\ x_{2}^{\prime }\relax (t )&=2 x_{1}\relax (t )-\frac {x_{2}\relax (t )}{2} \end {align*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 46
dsolve([diff(x__1(t),t)=-1/2*x__1(t)-1/8*x__2(t),diff(x__2(t),t)=2*x__1(t)-1/2*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {{\mathrm e}^{-\frac {t}{2}} \left (\cos \left (\frac {t}{2}\right ) c_{1}-\sin \left (\frac {t}{2}\right ) c_{2}\right )}{4} \] \[ x_{2}\relax (t ) = {\mathrm e}^{-\frac {t}{2}} \left (c_{2} \cos \left (\frac {t}{2}\right )+c_{1} \sin \left (\frac {t}{2}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 68
DSolve[{x1'[t]==-1/2*x1[t]-1/8*x2[t],x2'[t]==2*x1[t]-1/2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{4} e^{-t/2} \left (4 c_1 \cos \left (\frac {t}{2}\right )-c_2 \sin \left (\frac {t}{2}\right )\right ) \\ \text {x2}(t)\to e^{-t/2} \left (c_2 \cos \left (\frac {t}{2}\right )+4 c_1 \sin \left (\frac {t}{2}\right )\right ) \\ \end{align*}