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## Homework Statement

https://www.physicsforums.com/attachments/upload_2016-11-25_8-51-19-png.109406/ [Broken]

Find the differential equation for Vo

Vin is a square wave

## Homework Equations

KCL/KVL

## The Attempt at a Solution

At Node V1:

##\frac{V_1-V_in}{R_1} + \frac{1}{L_1}\int_{0}^{t}(V_1-V_2) = 0##

At Node V2:

##\frac{1}{L_1}\int_{0}^{t}(V_2-V_1)+C_1*\dot{V_2}+\frac{V_2}{R_2}=0##

V2 = Vo

Differentiate equation 2 and solve for V1

##V_2-V_1+L_1C_1\ddot{V_2}+\frac{L_1\dot{V_2}}{R_2}##

##V_1=V_2+L_1C_1\ddot{V_2}+\frac{L_1\dot{V_2}}{R_2}##

Plug into equation 1

##\frac{V_2}{R_1}+\frac{L_1C_1\ddot{V_2}}{R_1}+\frac{L_1\dot{V_2}}{R_1R_2}+\frac{1}{L_1}\int_{0}^{t}(L_1C_1\ddot{V_2}+\frac{L_1\dot{V_2}}{R_2}=\frac{V_{in}}{R_1})##

Get rid of integral

##\frac{V_2}{R_1}+\frac{L_1C_1\ddot{V_2}}{R_1}+\frac{L_1\dot{V_2}}{R_1R_2}+C_1\dot{V_2}+\frac{{V_2}}{R_2}=\frac{V_{in}}{R_1}##

Multiply everything by ##\frac{R_1}{L_1C_1}##

##\frac{V_2}{L_1C_1}+\ddot{V_2}+\frac{\dot{V_2}}{C_1R_2}+\frac{R_1\dot{V_2}}{L_1}+\frac{R_1{V_2}}{L_1C_1R_2}=\frac{V_{in}}{L_1C_1}##

Is my work correct?

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