Internal problem ID [773]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.8, Repeated Eigenvalues. page 436
Problem number: 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-\frac {5 x_{1} \left (t \right )}{2}+\frac {3 x_{2} \left (t \right )}{2}\\ x_{2}^{\prime }\left (t \right )&=-\frac {3 x_{1} \left (t \right )}{2}+\frac {x_{2} \left (t \right )}{2} \end {align*}
With initial conditions \[ [x_{1} \left (0\right ) = 3, x_{2} \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve([diff(x__1(t),t) = -5/2*x__1(t)+3/2*x__2(t), diff(x__2(t),t) = -3/2*x__1(t)+1/2*x__2(t), x__1(0) = 3, x__2(0) = -1], singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-t} \left (-6 t +3\right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{-t} \left (-18 t -3\right )}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 31
DSolve[{x1'[t]==-5/2*x1[t]+3/2*x2[t],x2'[t]==-3/2*x1[t]+1/2*x2[t]},{x1[0]==3,x2[0]==-1},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-t} (3-6 t) \\ \text {x2}(t)\to -e^{-t} (6 t+1) \\ \end{align*}