Internal problem ID [775]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.8, Repeated Eigenvalues. page 436
Problem number: 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+9 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {align*}
With initial conditions \[ [x_{1} \left (0\right ) = 2, x_{2} \left (0\right ) = 4] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(x__1(t),t) = 3*x__1(t)+9*x__2(t), diff(x__2(t),t) = -x__1(t)-3*x__2(t), x__1(0) = 2, x__2(0) = 4], singsol=all)
\begin{align*} x_{1} \left (t \right ) &= 42 t +2 \\ x_{2} \left (t \right ) &= 4-14 t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[{x1'[t]==3*x1[t]+9*x2[t],x2'[t]==-1*x1[t]-3*x2[t]},{x1[0]==2,x2[0]==4},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to 42 t+2 \\ \text {x2}(t)\to 4-14 t \\ \end{align*}