General existence theorem: Difference between revisions
From Rice Wiki
No edit summary |
No edit summary |
||
| Line 2: | Line 2: | ||
Every [[Second order linear ODE|Second order linear homogeneous ODE]] with continuous coefficients has a fundamental set of solutions. | Every [[Second order linear ODE|Second order linear homogeneous ODE]] with continuous coefficients has a fundamental set of solutions. | ||
This is proven by handpicking | 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). | |||
Revision as of 23:04, 21 May 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).
