In the plot below I have .
The second graph of the plot shows that, for x = 1, the plot of has an infinite slope at (called the Poisson non-linear propagation solution).
I'm trying to show this analytically but not getting the right answer. I reproduce my steps below.
We want to show that for , has an infinite slope, i.e. .
we have , so
What I'm trying to show is , but that's clearly not possible from my result above.
Keen to hear where I'm going wrong. Thanks