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#1 2011-08-01 11:19:18

Au101
Member
Registered: 2010-12-01
Posts: 353

Proof of the general solution of a linear second order DE

Hi guys,

My textbook gives a specific instance, but doesn't provide a proof of the following result:

Suppose that we have a linear second order differential equation of the form:

Where a, b and c are constants and where

Since the auxiliary equation has two equal roots α, the general solution will be:

Where A and B are arbitrary constants.
My attempt is below, and I'd be very grateful if anybody could confirm and/or provide the standard proof:

Last edited by Au101 (2011-08-01 11:22:13)

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