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Topic: Solution to differential equation problem without e in the base?
Replies: 3   Last Post: Jul 5, 2013 10:16 AM

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grei

Posts: 124
Registered: 11/27/12
Re: Solution to differential equation problem without e in the base?
Posted: Jul 5, 2013 7:56 AM
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All "bases" are equivalent. That is we can write a^x in terms of base b using logarithms. Since b^(log_b(x))= x, we can write a^x= b^(log_b(a^x))= b^(x log_b(a)).

In particular, if we have the differential equation dy/dx= .008y, while we CAN integrate it as y= Ce^(.008x) we can also write it as C(e^(.008))^x= 1.0080320855042734311720736146086^x which is [b]approximately[/b] 1.008^x.



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