Internal problem ID [767]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.8, Repeated Eigenvalues. page 436
Problem number: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ x_{2}^{\prime }\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: 24
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[{x1'[t]==4*x1[t]-2*x2[t],x2'[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*}