Internal problem ID [795]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 9.1, The Phase Plane: Linear Systems. page 505
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1} \relax (t )-4 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=4 x_{1} \relax (t )-7 x_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve([diff(x__1(t),t)=1*x__1(t)-4*x__2(t),diff(x__2(t),t)=4*x__1(t)-7*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {{\mathrm e}^{-3 t} \left (4 c_{2} t +4 c_{1}+c_{2}\right )}{4} \] \[ x_{2} \relax (t ) = {\mathrm e}^{-3 t} \left (c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 46
DSolve[{x1'[t]==1*x1[t]-4*x2[t],x2'[t]==4*x1[t]-7*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-3 t} (4 c_1 t-4 c_2 t+c_1) \\ \text {x2}(t)\to e^{-3 t} (4 (c_1-c_2) t+c_2) \\ \end{align*}