Internal problem ID [800]
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: 9.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=3 x_{1}\relax (t )-4 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=x_{1}\relax (t )-x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 28
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)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = {\mathrm e}^{t} \left (2 c_{2} t +2 c_{1}+c_{2}\right ) \] \[ x_{2}\relax (t ) = {\mathrm e}^{t} \left (c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 41
DSolve[{x1'[t]==3*x1[t]-4*x2[t],x2'[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*}