Hi Experts,
Not entirely sure if this posting is more appropriate in the symbolic.math group or this group, but since it is a current calculation, I'm thinking its fine to post here as well. I am trying to figure out how to solve the following problem relating to a passive circuit in a closed loop described by the following differential equation:
L*dI/dt + R*I = Eo (intial Differential Equation)
The problem is to solve the equation when an initial current Io is flowing and a constant emf Eo is impressed on the circuit at time t =0. Using variables separation, I can arrive at:
dI / (Eo - R*I) = 1/L*dt
and then I integrate both sides:
-log(Eo-R*I)/R = R/L*t + C1 // note - only 1 log term
The published solution using the initial condition I(0) = Io is:
log(Eo-R*I) = R/L*t + log(Eo - R*Io) // note the 2nd log term
I am guessing that the additional log term is obtained by solving for the constant C1, but how ?
Any input would be greatly appreciated!
Thanks, Mike.