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