Internal problem ID [358]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 1.
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 )&=-x_{1} \left (t \right )-4 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 30
dsolve([diff(x__1(t),t)=-2*x__1(t)+1*x__2(t),diff(x__2(t),t)=-1*x__1(t)-4*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \left (t \right ) = -{\mathrm e}^{-3 t} \left (c_{2} t +c_{1} +c_{2} \right ) \] \[ x_{2} \left (t \right ) = {\mathrm e}^{-3 t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 42
DSolve[{x1'[t]==-2*x1[t]+1*x2[t],x2'[t]==-1*x1[t]-4*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-3 t} (c_1 (t+1)+c_2 t) \\ \text {x2}(t)\to e^{-3 t} (c_2-(c_1+c_2) t) \\ \end{align*}