Engineering OpAmp Circuit Analysis: Finding the Differential Equation for Vo

[eehelp150]

If you combine your first and fourth equations, the derivatives can disappear and you will be left with V₂ in terms of things you know.

$\frac{V_1-V_{in}}{R_1}+\frac{V_1-V_p}{R_2}+\frac{V_2}{R_6}+\frac{V_2-V_o}{R_5}=0$

becomes

$\frac{\frac{R_3V_O}{R_3+R_4}+R_2C_1(\frac{R_3\dot{V_O}}{R_3+R_4})-V_{in}}{R_1}+\frac{R_2C_1(\frac{R_3\dot{V_O}}{R_3+R_4})}{R_2}+\frac{V_2}{R_6}+\frac{V_2-V_o}{R_5}=0$
How would I get rid of V2?

 

[NascentOxygen]

Isolate V₂. Determine $\dot V_2$.

Now you can substitute for all necessary terms so as to leave you with an equation relating V_o to V_in.

 

[eehelp150]

Isolate V₂. Determine $\dot V_2$.

Now you can substitute for all necessary terms so as to leave you with an equation relating V_o to V_in.

I'm not really following. There is no other equation with V2.

 

[The Electrician]

If you use the D operator technique, I think you will improve your ability to solve the system:

http://www.codecogs.com/library/maths/calculus/differential/linear-simultaneous-equations.php

http://www.solitaryroad.com/c658.html

 

[eehelp150]

If you use the D operator technique, I think you will improve your ability to solve the system:

http://www.codecogs.com/library/maths/calculus/differential/linear-simultaneous-equations.php

http://www.solitaryroad.com/c658.html

Even with d operators, how would I get rid of V2? There is only one equation with V2
If I combine NodeV2 and NodeV1, I get rid of the derivatives.
If I derive the combined equation and then solve NodeV1 for V_2' and plug into get rid of V_2', would that work?

 

[NascentOxygen]

If I derive the combined equation and then solve NodeV1 for V_2' and plug into get rid of V_2', would that work?

That's what I've been anticipating.

 

[rude man]

You seem to want to 'get rid of derivatives'. You can't. In fact the problem asks for the differential equation for Vo. That will include time derivatives of Vo and/or Vin.

Had you been asked to find Vo itself that would mean solving the diff. eq. But you weren't given an expression for Vin so you can't solve for Vo.