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Electronics/circuit question


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I have a simple example from my physics text using a separable ODE, but I don't understand the steps that they took to solve it.  It should be pretty straightforward, but I am getting something different when I try to solve.  I've attached the image of the page where my questions are, and a red "1" and "2" indicates my problems with it.

Note:  C = capacitor, E = emf of battery, q = charge in circuit

#1:  I don't understand how they got the final answer here.  If you multiply (CE - q)/RC by -1, you'd get (q-CE)/RC.  So how did they get -(q-CE)/RC ?  Seems like there's an extra negative sign.

#2:  I don't understand the integral solved on the left side of int((dq/(q-CE)) to get what they have for ln((q-CE)/(-C)).

I would have thought that int((dq/(q-CE)) = ln(q-CE)

I know these seem simple, but an I missing something obvious here in these?

In red 1, CE-q numerator, they just pulled out the "-" and made it -(-CE+q) = -(CE-q).

In #2, same type of arithmetic, just manipulate the equation without changing its quantity; remember you can do the same thing to each side of an equation and it doesn't effect the result.

Hope this helps.  


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IEEE (Institute of Electrical and Electronics Engineers); Senior Life member AES (Audio Engineering Society), Fellow Life member

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