#### The Electrician

Gold Member

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How about trying this:##\frac{V_N}{R_3}+\frac{V_N-V_O}{R_4}=0##

##V_N=V_P##

##\frac{V_P}{R_3}+\frac{V_P-V_O}{R_4}=0##

##V_P(1+\frac{R_4}{R_3})-V_O=0##

Solve eq1 for Vp

##V_P = \frac{R_2}{R_1}(V_1-V_{in})+V_1+C_2R_2(\dot{V_1}-\dot{V_2})##

Plug into earlier equation

##V_P(1+\frac{R_4}{R_3})-V_O=0##

##(\frac{R_2}{R_1}(V_1-V_{in})+V_1+C_2R_2(\dot{V_1}-\dot{V_2}))(1+\frac{R_4}{R_3})-V_O=0##

Expand

##\frac{R_2}{R_1}(V_1-V_{in})+V_1+C_2R_2(\dot{V_1}-\dot{V_2})+\frac{R_4R_2}{R_3R_1}(V_1-V_{in})+\frac{R_4V_1}{R_3}+\frac{R_4C_2R_2(\dot{V_1}-\dot{V_2})}{R_3}-V_O=0##

solve eq2 for V_1

##C_1\dot{V_P}+\frac{V_P-V_1}{R_2}=0##

##V_1=V_P+R_2C_1\dot{V_P}##

derive

##\dot{V_1}=\dot{V_P}+R_2C_1\ddot{V_P}##

Am I on the right track? I still don't know how to get rid of ##V_2## and ##\dot{V_2}#

Solve this: ##\frac{V_P}{R_3}+\frac{V_P-V_O}{R_4}=0##

for Vp, then substitute that in: ##V_1=V_P+R_2C_1\dot{V_P}##