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 }\left (t \right )&=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (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)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{-2 t} \\ x_{2} \left (t \right ) &= 3 c_{1} {\mathrm e}^{3 t}+\frac {c_{2} {\mathrm e}^{-2 t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 73
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 (c_2 \left (6 e^{5 t}-1\right )-3 c_1 \left (e^{5 t}-1\right )\right ) \\ \end{align*}