How do the solutions of a differential equation form a vector space and its basis?

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Suppose that you are given a third order linear homogeneous differential equation as follows: u'''(t) au''(t) bu'(t) cu(t) = 0

Given that we are dealing with a third order ODE, we will have the following general solution: y= c1f(t) c2g(t) c3h(t)

Finding the roots of the equation you get something along the lines of three exponential functions e^x, which from my overall understanding yields a linear combination of the three exponential solutions. How would you go about showing that these three solutions form a vector space along with its basis?

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Bornofisais

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Posted: 9 years ago
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