The Question
Let's consider the Richards' differential equation (RDE) as written here below, from Wikipedia:
How does the RDE change if I add the lower asymptote "A" in the generalised logistic function as follows?
$$ Y(t) = \frac{K}{(1+Qe^{-\alpha\nu(t-t_0)})^{1/\nu}} + A $$
My Attempt
In order to add the lower asymptote "A" in the RDE, I first tried to solve the RDE, getting the generalised logistic function:
$$ Y'(t) = \alpha Y \biggl(1- \biggl(\frac{Y}{K} \biggr)^\nu \biggr) $$
$$ \alpha \int_{t_0}^t dt = \int \frac{dY}{Y \biggl(1- \biggl(\frac{Y}{K} \biggr)^\nu \biggr)} $$
$$ \alpha (t-t_0) = ln|Y| - \frac{ln\biggl|1-\biggl(\frac{Y}{K}\biggr)^\nu\biggr|}{\nu} $$
$$ \nu \alpha (t-t_0) = ln|Y|^\nu - ln\biggl|1-\biggl(\frac{Y}{K}\biggr)^\nu\biggr| $$
$$ - \nu \alpha (t-t_0) = - ln|Y|^\nu + ln\biggl|1-\biggl(\frac{Y} {K}\biggr)^\nu\biggr| + C $$
$$ - C - \nu \alpha (t-t_0) = ln\left| \frac{1-\biggl(\frac{Y} {K}\biggr)^\nu}{Y^\nu} \right| $$
$$ \pm e^{- C} e^{- \nu \alpha (t-t_0)} = \frac{1-\biggl(\frac{Y} {K}\biggr)^\nu}{Y^\nu} $$
$$ \pm e^{- C} e^{- \nu \alpha (t-t_0)} = \biggl( 1-\biggl(\frac{Y} {K}\biggr)^\nu \biggr) \frac{1}{Y^\nu} $$
$$ \pm e^{- C} e^{- \nu \alpha (t-t_0)} = \frac{1}{Y^\nu} - \frac{1}{K^\nu} $$
I use: $W = \pm e^{- C}$
$$ \frac{1}{K^\nu} + W e^{- \nu \alpha (t-t_0)} = \frac{1}{Y^\nu} $$
$$ \frac{1 + K^\nu W e^{- \nu \alpha (t-t_0)}}{K^\nu} = \frac{1}{Y^\nu} $$
$$ Y^\nu = \frac{K^\nu}{1 + K^\nu W e^{- \nu \alpha (t-t_0)}} $$
I use: $Q = K^\nu W$
$$ Y^\nu = \frac{K^\nu}{1 + Q e^{- \nu \alpha (t-t_0)}} $$
$$ Y = \frac{K}{\biggl( 1 + Q e^{- \nu \alpha (t-t_0)}\biggr)^{1/\nu}} $$
Any suggestions or ideas to get the RDE, using the lower asymptote "A" in the generalised logistic function, as follows?
$$ Y(t) = \frac{K}{(1+Qe^{-\alpha\nu(t-t_0)})^{1/\nu}} + A $$
Note: I also found something close to my case, but I am not able to combine it with the exponent $1/\nu$ in my generalised logistic function. Ideas? (reference: Oliver, F. (1969). Another Generalisation of the Logistic Growth Function. Econometrica, 37(1), 144-147. doi:10.2307/1909213):
