17.10 problem 10

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 }\relax (t )&=3 x_{1}\relax (t )+9 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-x_{1}\relax (t )-3 x_{2}\relax (t ) \end {align*}

With initial conditions \[ [x_{1}\relax (0) = 2, x_{2}\relax (0) = 4] \]

Solution by Maple

Time used: 0.02 (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],[x__1(t), x__2(t)], singsol=all)
 

\[ x_{1}\relax (t ) = 42 t +2 \] \[ x_{2}\relax (t ) = -14 t +4 \]

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*}