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Trying2Learn
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- TL;DR Summary
- Why is the solution of a diff.eq. a vector space
Good Morning
Recently, I asked why there must be two possible solutions to a second order differential equation. I was very happy with the discussion and learned a lot -- thank you.
In it, someone wrote:
" It is a theorem in mathematics that the set of all functions that are solutions of a linear differential equation is a vector space , sub space of the vector space of all functions (of a real variable). "
Is there a chance someone could provide the name of this theorem and provide link (preferably on-line) to a simple, introductory discussion about it?
Recently, I asked why there must be two possible solutions to a second order differential equation. I was very happy with the discussion and learned a lot -- thank you.
In it, someone wrote:
" It is a theorem in mathematics that the set of all functions that are solutions of a linear differential equation is a vector space , sub space of the vector space of all functions (of a real variable). "
Is there a chance someone could provide the name of this theorem and provide link (preferably on-line) to a simple, introductory discussion about it?