Internal problem ID [1840]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.9, Systems of differential equations. Complex roots. Page 344
Problem number: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )-3 x_{2} \left (t \right ) \end {align*}
With initial conditions \[ [x_{1} \left (0\right ) = 1, x_{2} \left (0\right ) = 2] \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve([diff(x__1(t),t) = x__1(t)-x__2(t), diff(x__2(t),t) = 5*x__1(t)-3*x__2(t), x__1(0) = 1, x__2(0) = 2], singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-t} \cos \left (t \right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{-t} \left (-2 \cos \left (t \right )-\sin \left (t \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 29
DSolve[{x1'[t]==1*x1[t]-1*x2[t],x2'[t]==5*x1[t]-3*x2[t]},{x1[0]==1,x2[0]==2},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-t} \cos (t) \\ \text {x2}(t)\to e^{-t} (\sin (t)+2 \cos (t)) \\ \end{align*}