Internal problem ID [799]
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: 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-x_{1} \relax (t )-x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-\frac {5 x_{2} \relax (t )}{2} \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 28
dsolve([diff(x__1(t),t)=-1*x__1(t)-1*x__2(t),diff(x__2(t),t)=0*x__1(t)-25/10*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {2 c_{2} {\mathrm e}^{-\frac {5 t}{2}}}{3}+{\mathrm e}^{-t} c_{1} \] \[ x_{2} \relax (t ) = c_{2} {\mathrm e}^{-\frac {5 t}{2}} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 47
DSolve[{x1'[t]==-1*x1[t]-1*x2[t],x2'[t]==0*x1[t]-25/10*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \left (c_1-\frac {2 c_2}{3}\right ) e^{-t}+\frac {2}{3} c_2 e^{-5 t/2} \\ \text {x2}(t)\to c_2 e^{-5 t/2} \\ \end{align*}