10.17.10 problem 10

Internal problem ID [1425]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 7.8, Repeated Eigenvalues. page 436
Problem number : 10
Date solved : Monday, January 27, 2025 at 04:57:07 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )+9 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) = 2\\ x_{2} \left (0\right ) = 4 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 17

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[{D[ x1[t],t]==3*x1[t]+9*x2[t],D[ x2[t],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*}