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?