first order circuit are those circuits whose response can be expressed by a first order differential equations.
Example of such circuits include the RL and RC circuits
RL circuit : circuit that contains an indicator and a resistor.
RC circuit : circuit that contains a capacitor and resistor
This is a first order linear ordinary non-homogenous differential
equation describing the response of the capacitor voltage.
It is first order because the highest degree of derivative is one.
it is called linear because the differential equation is linear
function of (dvc /dt) and vc(t)
To solve this circuit I'm going to use the differential equation approach. I'm concerned with the
voltage across the capacitor at and
At position 1 before the switch is thrown
At position 2 after switch is thrown I have the following from KCL:
This reduces to:
My problem is that I know that this is correct but I don't know how to put it all together.
I know that the solution is of the form:
The answer is
How do I extract this from my work?