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 }\relax (t )&=3 x_{1}\relax (t )-2 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=4 x_{1}\relax (t )-x_{2}\relax (t ) \end {align*}
With initial conditions \[ [x_{1}\relax (0) = 1, x_{2}\relax (0) = 5] \]
✓ Solution by Maple
Time used: 0.033 (sec). Leaf size: 41
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],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {{\mathrm e}^{t} \left (2 \cos \left (2 t \right )-8 \sin \left (2 t \right )\right )}{2} \] \[ x_{2}\relax (t ) = {\mathrm e}^{t} \left (-3 \sin \left (2 t \right )+5 \cos \left (2 t \right )\right ) \]
✓ 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*}