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jychay2

  • 3 years ago

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

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  1. experimentX
    • 3 years ago
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    http://www.wolframalpha.com/input/?i=y%27%2B4y%3D60t

  2. Mimi_x3
    • 3 years ago
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    \[\frac{dv}{dt} = 60t - 4v\] \[\frac{dv}{dt} + 4v = 60t\] so find the integratiing factor \[ u = e^\int{4v}\]

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

  4. Mimi_x3
    • 3 years ago
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    yeah lol sorry; typo

  5. Mimi_x3
    • 3 years ago
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    \[\frac{dv}{dt} \left(e^{4t}\right) + 4\left(e^{4t}\right) v= 60t(e^{4t}) \] \[\frac{dv}{dt} \left(e^{4t}\right) +\left(e^{4t}\right)'v =60t\left(e^{4t}\right) \] \[\left(e^{4t}v\right) '= 60t\left(e^{4t}\right) \] 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.

  6. jychay2
    • 3 years ago
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    Alright, I get it.Thx ^^

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