Question

Find a general solution for dv/dt= 60t-4v

Answer 1

http://www.wolframalpha.com/input/?i=y%27%2B4y%3D60t

Answer 2

\[\frac{dv}{dt} = 60t - 4v\]
\[\frac{dv}{dt} + 4v = 60t\]
so find the integratiing factor
\[ u = e^\int{4v}\]

Answer 3

Woops the integrating factor should be,\[\huge u=e^{\int\limits 4 dt}\] Without that silly v there.

Answer 4

yeah lol sorry; typo

Answer 5

\[\frac{dv}{dt} \left(e^{4t}\right) + 4\left(e^{4t}\right) v= 60t(e^{4t}) \]
\[\frac{dv}{dt} \left(e^{4t}\right) +\left(e^{4t}\right)'v =60t\left(e^{4t}\right) \]
\[\left(e^{4t}v\right) '= 60t\left(e^{4t}\right) \]
Integrate both sides.
\[\int\limits\left(e^{4t}v\right) ' = \int\limits60t\left(e^{4t}\right) dt\]
You should be able to do it now.

Answer 6

Alright, I get it.Thx ^^