How can I solve the following equation for i(t) analytically, using
partial fraction decomposition:  (I am having trouble separating the
variables)

B, Bp, D, Dp and a are constants

di/dt = i * [(1/4)*B + a - (B - D + Dp) + (B + D + Dp - Bp - a) * i]

Thanks!

My guess is:

number1=(1/4)*B + a - (B - D + Dp
number2=(B + D + Dp - Bp - a)
i=integral of i * [number1 + number2 * i]

I'm no expert though.

let x = (1/4)*B + a - (B - D + Dp
y = (B + D + Dp - Bp - a)
then di/dt = i(x + yi)
or di/[i(x + yi)] = dt
Let 1/[i(x + yi)] = e/i + f/(x + yi) .....partial fraction
then ex + eyi + fi = 1 from numerator implies
ex = 1 and i(ey + f) = 0 
thus e = 1/x and f = -ey = -y/x
Hence 

dt =  di     +  -y di
     -----      -------
      xi         x(x + yi)

integrating both sides gives

t = (1/x)ln|i| -(y/x)ln|x + yi| + (1/x)ln|c| where the last term added
is a constant in a convenient term
thus 
xt = ln|ic/(x + yi)|    which can be writen as 
exp(xt) = ic/(x + yi)
simplifying gives
i =    x
    ---------------
    -y + c[exp(-xt)]