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question about Paul's Math website on linear diff. eq.

Posted on 2008-10-20
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Last Modified: 2012-05-05
I'm looking at Paul's math page (Paul Dawkins of Lamar U) and on this page:
http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx
about 1/2 down in example 1 he says:
Question:
dv/dt = 9.8 - 0.196v
Solution:
dv/dt + 0.196v = 9.8
u(t) = e^(integral(0.196dt)) = e^0.196t
OK, I get it so far - but how do they get from this:
e^(0.196t) dv/dt + 0.196e^(0.196t)v = 9.8e^(0.196t)
to this:
(e^(0.196t)v)' = 9.8e^(0.196t)

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Question by:zliminator
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Accepted Solution

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Peter Kwan earned 250 total points
ID: 22765169
Just follow the logic from equation 4 to equation 5, by substituting "u(t)" with e^0.196t and "y" with "v".

This is because d(e^ct)/dt = c * e^ct => d(e^0.196t)/dt = 0.196 * (e^0.196t)
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