Internal problem ID [794]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
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)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \left (t \right ) = \frac {{\mathrm e}^{-t} c_{1}}{3}+c_{2} {\mathrm e}^{t} \] \[ x_{2} \left (t \right ) = {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 73
DSolve[{x1'[t]==2*x1[t]-1*x2[t],x2'[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*}