Internal problem ID [769]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.8, Repeated Eigenvalues. page 436
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-3 x_{1} \relax (t )+\frac {5 x_{2} \relax (t )}{2}\\ x_{2}^{\prime }\relax (t )&=-\frac {5 x_{1} \relax (t )}{2}+2 x_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 35
dsolve([diff(x__1(t),t)=-3*x__1(t)+5/2*x__2(t),diff(x__2(t),t)=-5/2*x__1(t)+2*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {{\mathrm e}^{-\frac {t}{2}} \left (5 c_{2} t +5 c_{1}-2 c_{2}\right )}{5} \] \[ x_{2} \relax (t ) = {\mathrm e}^{-\frac {t}{2}} \left (c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 58
DSolve[{x1'[t]==-3*x1[t]+5/2*x2[t],x2'[t]==-5/2*x1[t]+2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-t/2} (c_1 (2-5 t)+5 c_2 t) \\ \text {x2}(t)\to \frac {1}{2} e^{-t/2} (c_2 (5 t+2)-5 c_1 t) \\ \end{align*}