# Thread: nth order DEs- relationship btwn fundamental/general solutions and linear dependency?

1. ## nth order DEs- relationship btwn fundamental/general solutions and linear dependency?

Ok, quick conceptual question. The relationship between the fundamental set of solutions and linear dependency is that the fundamental set of solutions is comprised of linear independent solutions.

What about the general solution, i.e. any arbitrary linear combination of any fundamental set of solutions. What is the relationship between the general solution and linear dependency? Is there any?

This is probably an easy question/concept but for some reason my mind is being very foggy right now.

Thanks!

2. ## Re: nth order DEs- relationship btwn fundamental/general solutions and linear depende

The set of all solutions to an nth order linear homogeneous equation forms an n dimensional vector space. The "fundamental set of solutions" is a set of n functions that form a basis for that vector space and so they must be linearly independent.