Ok, so I am doing some basic circuit analysis and it's been awhile since I have done any diff. eq's so I need a little help here.
I have an RLC circuit with a 2.5 Ohm resistor, a 1 Henry Inductor and a 1 farad Capacitor all in series. With an input of 24*u(t) where u(t) is the unit step function.
So I derived the 2nd order differential equation of.
y'' + 2.5y' + y = 24
Now the transient solutions will be found with the characteristic equation:
r^2 + 2.5r +1 = 0
giving me roots of -.5 and -2 and a transient function:
y(t) = c1*e^-.5t + c2*e^-2t
Now I can't remember how to find the Particular solution, is it:
Y(t) = At*e^-t
then find Y'(t) and Y''(t) don't really remember where to go from there.
Am I moving in the right direction?