Internal problem ID [1841]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.9, Systems of differential equations. Complex roots. Page 344
Problem number: 6.
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 )&=4 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {align*}
With initial conditions \[ [x_{1} \left (0\right ) = 1, x_{2} \left (0\right ) = 5] \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve([diff(x__1(t),t) = 3*x__1(t)-2*x__2(t), diff(x__2(t),t) = 4*x__1(t)-x__2(t), x__1(0) = 1, x__2(0) = 5], singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{t} \left (-4 \sin \left (2 t \right )+\cos \left (2 t \right )\right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{t} \left (-5 \cos \left (2 t \right )+3 \sin \left (2 t \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 40
DSolve[{x1'[t]==3*x1[t]-2*x2[t],x2'[t]==4*x1[t]-1*x2[t]},{x1[0]==1,x2[0]==5},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^t (\cos (2 t)-4 \sin (2 t)) \\ \text {x2}(t)\to e^t (5 \cos (2 t)-3 \sin (2 t)) \\ \end{align*}