# Pacemaker differential equation

1. Feb 8, 2006

### itzela

Hi Guys... i'm trying to learn diff.eq on my own and i'm stuck on a problem and I don't even know where or how to begin:

the problem is: the pacemaker shown in the figure (first attatchment) is made up of an electric battery, a small capacitor, and the heart which functions like a resistence in the circuit. When the commuter S connects to P the capacitor charges, when S is connected to Q the capacitor discharges sending an electric shock to the heart. During this time the electric tension E applied to the heart is given by: (second attatchment).

The resistance and the capacitance are both constant...
what is:
E(t)= ? E(t1) = Eo

Would it be a first order linear equation?
Is it homogenous?
What would be the value of the initial voltage?

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2. Feb 8, 2006

### Tom Mattson

Staff Emeritus
I can't make out the commuter in the diagram. It looks like it could be just a switch that shuts out the resistor, leaving only the capacitor and inductor in series. If that is the case then the capacitor will certainly not be charged. Capacitors that are both in series and in parallel with a DC voltage source cannot be charged with that source.

What is $t_1$?

What is the definition of a first order equation? Of a linear equation? Of a homogeneous equation?

Once you look those up: Can you try to apply those definitions to your equation to see if it satisfies them?

Without a clearer diagram, I can't tell.

3. Feb 12, 2006

### itzela

Thanks Tom... i figured it out. It was actually quite simply, just a matter of separating the variables and differentiating.

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