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#### find_the_fun

##### Active member

- Feb 1, 2012

- 166

So I rewrite equation as \(\displaystyle \frac{di}{dt}+\frac{R}{L}i=\frac{E}{L}\) therefore \(\displaystyle P(i)=\frac{R}{L}\)

let \(\displaystyle \mu(x)=e^{\int \frac{R}{L}dt}=e^{\frac{tr}{L}+C}\)

multiply equation by integrating factor to get

\(\displaystyle e^{\frac{tR}{L}} \frac{di}{dt}+e^{\frac{tr}{L}} \frac{Ri}{L}=e^{\frac{tr}{L}}\frac{E}{L}\)

\(\displaystyle \frac{d}{dt}[\mu(x)i]=e^{\frac{tR}{L}}\frac{E}{L}i\)

I think I've done something wrong because the above statement is not true. Also, every question I've seen the e^some-integral involves ln so the e's go away. Is this always the case?