Internal problem ID [313]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.2, Matrices and Linear systems. Page 384
Problem number: problem 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 28
dsolve([diff(x__1(t),t)=4*x__1(t)+2*x__1(t),diff(x__2(t),t)=-3*x__1(t)-x__2(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{6 t} \\ x_{2} \left (t \right ) &= -\frac {3 c_{2} {\mathrm e}^{6 t}}{7}+{\mathrm e}^{-t} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 56
DSolve[{x1'[t]==4*x1[t]+2*x2[t],x2'[t]==-3*x1[t]-x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^t \left (c_1 \left (3 e^t-2\right )+2 c_2 \left (e^t-1\right )\right ) \\ \text {x2}(t)\to e^t \left (c_2 \left (3-2 e^t\right )-3 c_1 \left (e^t-1\right )\right ) \\ \end{align*}