Question

Need help explain mew for integrating factors on 1st order linear derivatives.

for example dv/dt = 9.8 - 0.196v

Answer 1

http://en.wikipedia.org/wiki/Integrating_factor

Answer 2

basically you try to find an integrating factor, such that, when both sides are multiplied by it, the left side turns into a derivative of something, which makes it easy to integrate.

Answer 3

rewrite your equation as:
v' = 9.8 - 0.196v
v' + 0.196v = 9.8
or in a more general sense,
v' + p(x)v = q(x), then \[\rho = e^ \left( \int\limits p(x) dx \right)\]
or mew, whichever symbol you're using.

Than if you multiply your integrating factor through the equation, you get a simple derivation on the left, namely

(mew*v)' = mew*q(x)

Then you integrate and win