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

Question

unklerhaukus · Answer

what is $L$ ?

anonymous · Answer

Linear DE operated on...

anonymous · Answer

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

unklerhaukus · Answer

i can not see the differential equation

anonymous · Answer

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

anonymous · Answer

Or is this only provable for more specific DE?

unklerhaukus · Answer

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

anonymous · Answer

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

anonymous · Answer

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

unklerhaukus · Answer

actually the roots are in the complementary solution