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## jychay2 2 years ago Find a general solution for dv/dt= 60t-4v

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1. experimentX
2. Mimi_x3

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

3. zepdrix

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

4. Mimi_x3

yeah lol sorry; typo

5. 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.

6. jychay2

Alright, I get it.Thx ^^

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