anonymous
  • anonymous
Find a general solution for dv/dt= 60t-4v
Mathematics
schrodinger
  • schrodinger
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experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=y%27%2B4y%3D60t
Mimi_x3
  • Mimi_x3
\[\frac{dv}{dt} = 60t - 4v\] \[\frac{dv}{dt} + 4v = 60t\] so find the integratiing factor \[ u = e^\int{4v}\]
zepdrix
  • zepdrix
Woops the integrating factor should be,\[\huge u=e^{\int\limits 4 dt}\] Without that silly v there.

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Mimi_x3
  • Mimi_x3
yeah lol sorry; typo
Mimi_x3
  • Mimi_x3
\[\frac{dv}{dt} \left(e^{4t}\right) + 4\left(e^{4t}\right) v= 60t(e^{4t}) \] \[\frac{dv}{dt} \left(e^{4t}\right) +\left(e^{4t}\right)'v =60t\left(e^{4t}\right) \] \[\left(e^{4t}v\right) '= 60t\left(e^{4t}\right) \] 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.
anonymous
  • anonymous
Alright, I get it.Thx ^^

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