How Do Differential Equations Model Electric Circuits in Medical Devices?

AI Thread Summary
Differential equations are essential for modeling electric circuits in medical devices like pacemakers, where components such as batteries, capacitors, and resistances interact. The problem involves determining the electric tension E applied to the heart over time, with the capacitor charging and discharging based on the switch's position. The discussion raises questions about the nature of the equation, specifically whether it is first-order linear and homogeneous, and seeks guidance on finding the initial voltage. Understanding these concepts is crucial for solving the problem effectively. Clarification on the problem may be needed for better assistance.
itzela
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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?

- i translated it directly from spanish so if further clarifying of the problem is needed please let me know.
 

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any advice on how to start?
 

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