Solve DE with secondary function

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I want to solve

$-F''(a) + g(a)( F'(a) - F(a)$

where $g(a)$ is logistic.

My code is

a = var('a')
g(a)= 1 /(1 + e^(-(a)))  
F = function('F', a)
de = -diff(F,a, 2) + g(a)*(diff(F,a,1) - F(a))
y = desolve(de, F); y

But I get an error (at the end of the post). If I remove e(a) from the de-term, I get a solution. What do I have to take into account when I add the second function?

TypeError: no canonical coercion from <class 'sage.symbolic.function_factory.NewSymbolicFunction'> to Symbolic Ring