10.19.8 problem 8

Internal problem ID [1449]
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
Date solved : Monday, January 27, 2025 at 04:57:29 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-\frac {5 x_{2} \left (t \right )}{2} \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 27

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)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= \frac {2 c_2 \,{\mathrm e}^{-\frac {5 t}{2}}}{3}+{\mathrm e}^{-t} c_1 \\ x_{2} \left (t \right ) &= c_2 \,{\mathrm e}^{-\frac {5 t}{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 47

DSolve[{D[ x1[t],t]==-1*x1[t]-1*x2[t],D[ x2[t],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*}