10.17.1 problem 1

Internal problem ID [1416]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 7.8, Repeated Eigenvalues. page 436
Problem number : 1
Date solved : Monday, January 27, 2025 at 04:57:00 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )-x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 30

dsolve([diff(x__1(t),t)=3*x__1(t)-4*x__2(t),diff(x__2(t),t)=1*x__1(t)-1*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{t} \left (c_2 t +c_1 \right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{t} \left (2 c_2 t +2 c_1 -c_2 \right )}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 41

DSolve[{D[ x1[t],t]==3*x1[t]-4*x2[t],D[ x2[t],t]==1*x1[t]-1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^t (2 c_1 t-4 c_2 t+c_1) \\ \text {x2}(t)\to e^t ((c_1-2 c_2) t+c_2) \\ \end{align*}