Question

desing a system that will solve any pd
\[p(D)=a_nD^n+a_{n-1}D^{n-1}+...+a_1D+a_0=Ae^{at}\]

Answer 1

\[\text{basically solve for } y \text{ if } D \text{ is the operator}\\ D^n=\frac{d^ny}{dx^n}\]

Answer 2

Seems tough unless you can solve high degree polynomials unless there's something here I'm not seeing.

Answer 3

https://en.wikipedia.org/wiki/Galois_theory

Answer 4

That means you can't use auxiliary...

Answer 5

You can do this, but you might have to settle for something that gives you numeric approximations I think.

Answer 6

there is a very nice formula for this, consider the pd
search onlne for something called ERF
exponent response formula

Answer 7

Very interesting, I'm looking into it now.

Answer 8

i am concerned with the proof...this is a very nice tool