Internal problem ID [792]
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: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=3 x_{1}\relax (t )-2 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=2 x_{1}\relax (t )-2 x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 36
dsolve([diff(x__1(t),t)=3*x__1(t)-2*x__2(t),diff(x__2(t),t)=2*x__1(t)-2*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {{\mathrm e}^{-t} c_{1}}{2}+2 c_{2} {\mathrm e}^{2 t} \] \[ x_{2}\relax (t ) = {\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 73
DSolve[{x1'[t]==3*x1[t]-2*x2[t],x2'[t]==2*x1[t]-2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{3} e^{-t} \left (c_1 \left (4 e^{3 t}-1\right )-2 c_2 \left (e^{3 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{3} e^{-t} \left (2 c_1 \left (e^{3 t}-1\right )-c_2 \left (e^{3 t}-4\right )\right ) \\ \end{align*}