Internal problem ID [1836]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.9, Systems of differential equations. Complex roots. Page 344
Problem number: 1.
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 )&=-x_{1}\relax (t )-x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 45
dsolve([diff(x__1(t),t)=-3*x__1(t)+2*x__2(t),diff(x__2(t),t)=-1*x__1(t)-1*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = {\mathrm e}^{-2 t} \left (c_{1} \sin \relax (t )+\sin \relax (t ) c_{2}-\cos \relax (t ) c_{1}+c_{2} \cos \relax (t )\right ) \] \[ x_{2}\relax (t ) = {\mathrm e}^{-2 t} \left (c_{1} \sin \relax (t )+c_{2} \cos \relax (t )\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 52
DSolve[{x1'[t]==-3*x1[t]+2*x2[t],x2'[t]==-1*x1[t]-1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-2 t} (c_1 \cos (t)-(c_1-2 c_2) \sin (t)) \\ \text {x2}(t)\to e^{-2 t} (c_2 (\sin (t)+\cos (t))-c_1 \sin (t)) \\ \end{align*}