## henpen Group Title Mathematically, prove that there are there no arbitrary constants required for the particular solution of $Ly=f(x)$. one year ago one year ago

1. UnkleRhaukus Group Title

what is $$L$$ ?

2. henpen Group Title

Linear DE operated on...

3. henpen Group Title

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

4. UnkleRhaukus Group Title

i can not see the differential equation

5. henpen Group Title

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

6. henpen Group Title

Or is this only provable for more specific DE?

7. UnkleRhaukus Group Title

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

8. henpen Group Title

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

9. henpen Group Title

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

10. UnkleRhaukus Group Title

actually the roots are in the complementary solution