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

Question

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

anonymous · Answer

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

kainui · Answer

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

kc_kennylau · Answer

kc_kennylau · Answer

That means you can't use auxiliary...

kainui · Answer

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

anonymous · Answer

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

kainui · Answer

Very interesting, I'm looking into it now.

anonymous · Answer

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