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

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henpen
 2 years ago
Best ResponseYou've already chosen the best response.0Linear DE operated on...

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0I know that it's obvious, but I've yet to encounter a formal proof.

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0i can not see the differential equation

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0Oh, it's just the general sign for\[Ly=\sum_{i=0}^{i=n}a_i\frac{d^i}{dx^i}y=0\]

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0Or is this only provable for more specific DE?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0i thought there were usually as many constants in the solution as the order of the DE

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, but they're all in the complimentary solution.

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0I've not come across 'roots' with regards to DE, but I suppose so, yes.

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0actually the roots are in the complementary solution
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