10.17.2 problem 2

Internal problem ID [1417]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 7.8, Repeated Eigenvalues. page 436
Problem number : 2
Date solved : Monday, January 27, 2025 at 04:57:01 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=4 x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=8 x_{1} \left (t \right )-4 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 23

dsolve([diff(x__1(t),t)=4*x__1(t)-2*x__2(t),diff(x__2(t),t)=8*x__1(t)-4*x__2(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 34

DSolve[{D[ x1[t],t]==4*x1[t]-2*x2[t],D[ x2[t],t]==8*x1[t]-4*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to 4 c_1 t-2 c_2 t+c_1 \\ \text {x2}(t)\to 8 c_1 t-4 c_2 t+c_2 \\ \end{align*}