Internal problem ID [754]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.6, Complex Eigenvalues. page 417
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=2 x_{1}\relax (t )-\frac {5 x_{2}\relax (t )}{2}\\ x_{2}^{\prime }\relax (t )&=\frac {9 x_{1}\relax (t )}{5}-x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 58
dsolve([diff(x__1(t),t)=2*x__1(t)-5/2*x__2(t),diff(x__2(t),t)=9/5*x__1(t)-1*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {5 \,{\mathrm e}^{\frac {t}{2}} \left (\sin \left (\frac {3 t}{2}\right ) c_{1}-\sin \left (\frac {3 t}{2}\right ) c_{2}+\cos \left (\frac {3 t}{2}\right ) c_{1}+\cos \left (\frac {3 t}{2}\right ) c_{2}\right )}{6} \] \[ x_{2}\relax (t ) = {\mathrm e}^{\frac {t}{2}} \left (\sin \left (\frac {3 t}{2}\right ) c_{1}+\cos \left (\frac {3 t}{2}\right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 84
DSolve[{x1'[t]==2*x1[t]-5/2*x2[t],x2'[t]==9/5*x1[t]-1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{3} e^{t/2} \left (3 c_1 \cos \left (\frac {3 t}{2}\right )+(3 c_1-5 c_2) \sin \left (\frac {3 t}{2}\right )\right ) \\ \text {x2}(t)\to \frac {1}{5} e^{t/2} \left (5 c_2 \cos \left (\frac {3 t}{2}\right )+(6 c_1-5 c_2) \sin \left (\frac {3 t}{2}\right )\right ) \\ \end{align*}