Question

Mathematically, prove that there are there no arbitrary constants required for the particular solution of \[Ly=f(x)\].

Answer 1

what is \(L\) ?

Answer 2

Linear DE operated on...

Answer 3

I know that it's obvious, but I've yet to encounter a formal proof.

Answer 4

i can not see the differential equation

Answer 5

Oh, it's just the general sign for\[Ly=\sum_{i=0}^{i=n}a_i\frac{d^i}{dx^i}y=0\]

Answer 6

Or is this only provable for more specific DE?

Answer 7

i thought there were usually as many constants in the solution as the order of the DE

Answer 8

Yes, but they're all in the complimentary solution.

Answer 9

I've not come across 'roots' with regards to DE, but I suppose so, yes.

Answer 10

actually the roots are in the complementary solution