There are a few theorems in my DE book whose proofs I've been trying to find, without much luck:(adsbygoogle = window.adsbygoogle || []).push({});

1) Given an nth order linear homogenous ODE with continuous coefficients and nonzero leading coefficient, any IVP of this ODE has a unique solution over some interval I centered about the IVP.

2) Abel's Theorem for nth order linear homogenous ODE: Given an nth order linear homogenous ODE with continuous coefficients and nonzero leading coefficient, if [itex] \{y_{1},y_{2}...y_{n} \}[/itex] are all solutions to the ODE on some interval I, and they have derivatives up to order (n-1) on I, then their Wronskian is either 0 everywhere on I or nonzero everywhere on I.

3) Every nth order linear homogenous ODE with continuous coefficients and nonzero leading coefficient has a fundamental set.

In what textbook might I find a proof of these theorems? Thanks!

BiP

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# Where can I find proofs of these theorems?

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