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Second Order Differential equations help

Suppose your auxiliary equation was m2+5m+6mm^2 + 5m + 6m then factorised it to get (m+3)(m+2)(m+3)(m+2) so your two solutions are m=2m=-2 and m=3m=-3

When writing the complementary function, does the order of the roots matter in the power?

So is y=Ae2x+Be3xy = Ae^{-2x} + Be^{-3x} the same as y=Ae3x+Be2xy = Ae^{-3x} + Be^{-2x}

I know it sounds like a silly question but A and B could be different values so both complementary functions wouldn't be the same
Reply 1
Original post by ManLike007
Suppose your auxiliary equation was m2+5m+6mm^2 + 5m + 6m then factorised it to get (m+3)(m+2)(m+3)(m+2) so your two solutions are m=2m=-2 and m=3m=-3

When writing the complementary function, does the order of the roots matter in the power?

So is y=Ae2x+Be3xy = Ae^{-2x} + Be^{-3x} the same as y=Ae3x+Be2xy = Ae^{-3x} + Be^{-2x}

I know it sounds like a silly question but A and B could be different values so both complementary functions wouldn't be the same


Doesn't matter as when the particular solution is found A and B just become integers
You choose either to start with, and then stick with one of them consistently throughout the question.

EDIT: so the order doesn't matter to start with, but once you've chosen a certain order, you have to stick with it for that question.
(edited 6 years ago)
go with A and B.... although you may find in the answer section they have used B and A or maybe C & D etc.
Original post by RBP_98
Doesn't matter as when the particular solution is found A and B just become integers
It's true that it doesn't matter, but at the same time there's no reason to expect A and B to end up as integers.
Reply 5
Original post by DFranklin
It's true that it doesn't matter, but at the same time there's no reason to expect A and B to end up as integers.


Sorry yes that is completely true, meant to say as constants! Two years learning this stuff and I forget in about two weeks

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