General existence theorem: Difference between revisions
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Now that we have the two, every other IVP is solved (pretty easily because variables are nice). | Now that we have the two, every other IVP is solved (pretty easily because variables are nice). | ||
This also works for [[systems of ODEs]]. | |||
Revision as of 14:52, 10 June 2024
Every Second order linear homogeneous ODE with continuous coefficients has a fundamental set of solutions.
This is proven by handpicking two sets of initial conditions such that the Wronskian is 1 for two specific solutions to the homogeneous.
Now that we have the two, every other IVP is solved (pretty easily because variables are nice).
This also works for systems of ODEs.
