- #1

Nat3

- 69

- 0

## Homework Statement

Derive the differential equation from the following circuit

## Homework Equations

The solution needs to be a differential equation in standard form, so that I can solve the equation for the characteristic modes, zero-input response, zero-state response, etc.

## The Attempt at a Solution

For the first op amp, I did this:

[itex]\frac{x(t)-0}{R_1} = C_1\frac{dV_{C_1}}{dt}[/itex]

[itex]V_{C1} = 0 - y_1(t) = -y_1(t)[/itex]

[itex]\frac{x(t)}{R_1} = C_1\frac{dy_1(t)}{dt}[/itex]

[itex]\frac{dy_1(t)}{dt} = \frac{x(t)}{R_1C_1}[/itex]

Then, for the second op amp:

[itex]\frac{y_1(t)}{R_2} = C_2\frac{dV_{C_2}}{dt} + \frac{0-y(t)}{R_3}[/itex]

[itex]V_{C_2}=0-y(t)[/itex]

[itex]\frac{y_1(t)}{R_2} = -C_2\frac{dy(t)}{dt} - \frac{y(t)}{R_3}[/itex]

At this point, I'm stuck.

Any help would be greatly appreciated!