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## Homework Statement

http://imageshack.com/a/img580/682/z3mt.jpg

Derive a linear differential equation for the above LTI system.

## Homework Equations

[itex]i_C=C\frac{dV_C(t)}{dt}[/itex]

[itex]V_L=L\frac{di_L(t)}{dt}[/itex]

## The Attempt at a Solution

Using KVL, I can get the following equation:

[itex]V_{in}(t)=L\frac{di(t)_L}{dt}+i(t)R_A+\int\frac{i(t)}{C}dt+V_o(t)[/itex]

However, I don't know where to go from here. All of the differential equations describing LTI systems in my textbook look like:

[itex]ay'' + by' + cy = g(x)[/itex]

Or something similar to that, and then we factor out the y to get something like

[itex](aD^2+bD+c)y = g(x)[/itex]

Then we factor what's in the parenthesis to find the characteristic roots.

Any advice on how to proceed?