View source for Homogeneous linear systems: constant coefficients

[[Category:Differential Equations]]

Homogeneous linear systems of [[ODE]]s take the following form:

<math>
\vec{x}'=Ax
</math>

Similar to the scalar case, we look for some exponential solutions:

<math>
\vec{x}=e^{rt}\vec{\xi }
</math>

Doing some basic differentiation and substitution from the above two equations, we get

<math>
r\vec{\xi}=A\vec{\xi}
</math>