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[SOLVED] Simple RC circuit equation

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AssemblyLine

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Can anybody help me findind the differential equation for Vout in this tricky RC circuit?
If possibly working with letter not with absolute values
I tried several times but I am stuck
I think I am spinning around the tail;
I have write all the possible relations involved(KVL KCL ,voltage nodes method, imaginary currents metod)
But I can't find it!
Please help!
Circuit is attached
View attachment untitled.bmp
 

attachment.php


Calling Vn the central node and applying the Millman theorem:

\[V_n = \frac{V_1 sC_1 }{sC_1+\frac{1}{R_1}+\frac{1}{R_2+\frac{1}{s C_2}}}\]

and

\[V_o = \frac{\frac{V_n}{R_2}}{\frac{1}{R_2}+ sC_2}\]

replacing-arranging

\[V_o = \frac{C_1R_1s\;V_1}{C_1C_2R_1R_2\;s^2 + (C_1R_1 + C_2(R_1 + R_2))s + 1 }\]

and it's easy convert to the differential form.
 

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Thank you a lot!
I did not heard until now about Millman theorem(or I didn't know it is called that way)
Thank you ,again!
 

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