anonymous
  • anonymous
Mathematically, prove that there are there no arbitrary constants required for the particular solution of \[Ly=f(x)\].
Mathematics
jamiebookeater
  • jamiebookeater
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UnkleRhaukus
  • UnkleRhaukus
what is \(L\) ?
anonymous
  • anonymous
Linear DE operated on...
anonymous
  • anonymous
I know that it's obvious, but I've yet to encounter a formal proof.

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UnkleRhaukus
  • UnkleRhaukus
i can not see the differential equation
anonymous
  • anonymous
Oh, it's just the general sign for\[Ly=\sum_{i=0}^{i=n}a_i\frac{d^i}{dx^i}y=0\]
anonymous
  • anonymous
Or is this only provable for more specific DE?
UnkleRhaukus
  • UnkleRhaukus
i thought there were usually as many constants in the solution as the order of the DE
anonymous
  • anonymous
Yes, but they're all in the complimentary solution.
anonymous
  • anonymous
I've not come across 'roots' with regards to DE, but I suppose so, yes.
UnkleRhaukus
  • UnkleRhaukus
actually the roots are in the complementary solution

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