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everyone. I am trying to solve the following differential equation using the Laplace Transform:

$L\frac{di}{dt} + Ri = E$

I have managed to reduce it to the following equation:

$I(s) = \frac{E}{sL(s+R/L)}$

But I'm having a problem with it from there. Can somebody help me solve this please? Any help would be much appreciated.

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    What you can do at this stage is use a [decomposition in partial fractions](http://en.wikipedia.org/wiki/Partial_fraction) to simplify your solution so that you can easily transform it back.2012-02-07

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Your equation has a very simple solution given by

$i(t)=Ae^{-\frac{R}{L}t}+\frac{E}{R}$

being $A$ an arbitrary constant. Now, take a look at your Laplace transform

$I(s)=\frac{E}{sL\left(s+\frac{R}{L}\right)}$

and you will recognize two poles for $s=0$ and $s=-\frac{R}{L}$. The first pole will give rise to the constant term while the other one is just the exponential contribution. Indeed, here you can find a table of well-known transformed functions. This is essential in circuit analysis. Your case is the "exponential approach".