Internal problem ID [772]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.8, Repeated Eigenvalues. page 436
Problem number: 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )-7 x_{2} \left (t \right ) \end {align*}
With initial conditions \[ [x_{1} \left (0\right ) = 3, x_{2} \left (0\right ) = 2] \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve([diff(x__1(t),t) = x__1(t)-4*x__2(t), diff(x__2(t),t) = 4*x__1(t)-7*x__2(t), x__1(0) = 3, x__2(0) = 2], singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-3 t} \left (4 t +3\right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{-3 t} \left (16 t +8\right )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 34
DSolve[{x1'[t]==1*x1[t]-4*x2[t],x2'[t]==1*x1[t]-4*x2[t]},{x1[0]==3,x2[0]==2},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {5 e^{-3 t}}{3}+\frac {4}{3} \\ \text {x2}(t)\to \frac {5 e^{-3 t}}{3}+\frac {1}{3} \\ \end{align*}