# Homework Help: Simple Electrical Modeling Question (w/ only C and L)

1. Jan 24, 2016

### Bluestribute

1. The problem statement, all variables and given/known data
Find a differential equation that describes the circuit that includes only vin and vout as variables.

2. Relevant equations
C(dvin - dvout)/dt = i
vin - vout = L(di/dt)

3. The attempt at a solution
So the answer I got was:

C(d2vout/dt2) + vout = LC(d2vin/dt2)

My question is, is it allowable to break up the capacitor derivate like that? After substituting in for i, I got:

vout = Ld/dt(C(dvin - dvout)/dt)

Then I broke up the capacitor into vin and vout terms and just rearranged. But I'm not 100% sure if that's legal.

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2. Jan 24, 2016

### Staff: Mentor

That first C should be LC.

A rule of the Calculus says that the derivative of a sum equals the sum of the separate derivatives, so your approach is correct.

3. Jan 24, 2016

### Bluestribute

Woopsie, right. LC

Ok sweet, thanks. I just can't remember something we might have glossed over a few years ago . . . and no one recently has said "You can do this to a derivative". They just sorta do it on their own.