I just came from a class lecture that tied together the relationship between linear algebra and differential equations. The lecture dealt only with homogeneous linear equations. I understood about 90% of it and want to try to tie together the loose ends.(adsbygoogle = window.adsbygoogle || []).push({});

In a nutshell, if I have a homogeneous linear differential equation of degree n, where L is a linear differential operator of order n. Then the general solution of the homogeneous linear differential equation is the linear combination of n linearly independent elements of ker(L).

I haven't seen this applied to an example yet, so it's not entirely clear, but have I stated the relationship correctly?

I guess I'll see examples tomorrow, but I'd like to go into class with a crystal clear picture, so I can following along with what will probably be another lightning quick lecture.

Can anyone provide a simple example?

Thanks.

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# Relationship between Linear Algebra and Differential equations

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