## henpen 2 years ago Mathematically, prove that there are there no arbitrary constants required for the particular solution of $Ly=f(x)$.

1. UnkleRhaukus

what is $$L$$ ?

2. henpen

Linear DE operated on...

3. henpen

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

4. UnkleRhaukus

i can not see the differential equation

5. henpen

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

Or is this only provable for more specific DE?

7. UnkleRhaukus

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

8. henpen

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

9. henpen

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

10. UnkleRhaukus

actually the roots are in the complementary solution