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

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henpenBest ResponseYou've already chosen the best response.0
Linear DE operated on...
 one year ago

henpenBest ResponseYou've already chosen the best response.0
I know that it's obvious, but I've yet to encounter a formal proof.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
i can not see the differential equation
 one year ago

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

henpenBest ResponseYou've already chosen the best response.0
Or is this only provable for more specific DE?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
i thought there were usually as many constants in the solution as the order of the DE
 one year ago

henpenBest ResponseYou've already chosen the best response.0
Yes, but they're all in the complimentary solution.
 one year ago

henpenBest ResponseYou've already chosen the best response.0
I've not come across 'roots' with regards to DE, but I suppose so, yes.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
actually the roots are in the complementary solution
 one year ago
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