Internal problem ID [314]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.2, Matrices and Linear systems. Page 384
Problem number: problem 14.
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 )&=-3 x_{1}\relax (t )+4 x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 36
dsolve([diff(x__1(t),t)=-3*x__1(t)+2*x__2(t),diff(x__2(t),t)=-3*x__1(t)+4*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {c_{1} {\mathrm e}^{3 t}}{3}+2 \,{\mathrm e}^{-2 t} c_{2} \] \[ x_{2}\relax (t ) = c_{1} {\mathrm e}^{3 t}+{\mathrm e}^{-2 t} c_{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 72
DSolve[{x1'[t]==-3*x1[t]+2*x2[t],x2'[t]==-3*x1[t]+4*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{5} e^{-2 t} \left (2 c_2 \left (e^{5 t}-1\right )-c_1 \left (e^{5 t}-6\right )\right ) \\ \text {x2}(t)\to \frac {1}{5} e^{-2 t} \left (-3 (c_1-2 c_2) e^{5 t}+3 c_1-c_2\right ) \\ \end{align*}