10.17.8 problem 8

Internal problem ID [1423]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 7.8, Repeated Eigenvalues. page 436
Problem number : 8
Date solved : Monday, January 27, 2025 at 04:57:06 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-\frac {5 x_{1} \left (t \right )}{2}+\frac {3 x_{2} \left (t \right )}{2}\\ \frac {d}{d t}x_{2} \left (t \right )&=-\frac {3 x_{1} \left (t \right )}{2}+\frac {x_{2} \left (t \right )}{2} \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) = 3\\ x_{2} \left (0\right ) = -1 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 28

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[{D[ x1[t],t]==-5/2*x1[t]+3/2*x2[t],D[ x2[t],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*}