10.19.3 problem 3

Internal problem ID [1444]
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 : 3
Date solved : Monday, January 27, 2025 at 04:57:25 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 30

dsolve([diff(x__1(t),t)=2*x__1(t)-1*x__2(t),diff(x__2(t),t)=3*x__1(t)-2*x__2(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 73

DSolve[{D[ x1[t],t]==2*x1[t]-1*x2[t],D[ x2[t],t]==3*x1[t]-2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-t} \left (c_1 \left (3 e^{2 t}-1\right )-c_2 \left (e^{2 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{2} e^{-t} \left (3 c_1 \left (e^{2 t}-1\right )-c_2 \left (e^{2 t}-3\right )\right ) \\ \end{align*}