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 }\left (t \right )&=-3 x_{1} \left (t \right )+\frac {5 x_{2} \left (t \right )}{2}\\ x_{2}^{\prime }\left (t \right )&=-\frac {5 x_{1} \left (t \right )}{2}+2 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-\frac {t}{2}} \left (c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{-\frac {t}{2}} \left (5 c_{2} t +5 c_{1} +2 c_{2} \right )}{5} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 59
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} (-5 c_1 t+5 c_2 t+2 c_2) \\ \end{align*}