Homogeneous linear systems: constant coefficients: Difference between revisions
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(Created page with "Category:Differential Equations Homogeneous linear systems of ODEs 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>") |
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<math> | <math> | ||
\vec{x}=e^{rt}\vec{\xi } | \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> | </math> | ||
Revision as of 15:09, 10 June 2024
Homogeneous linear systems of ODEs take the following form:
Similar to the scalar case, we look for some exponential solutions:
Doing some basic differentiation and substitution from the above two equations, we get
