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2015-07-19 07:13:44 -0500 asked a question Solving this DE containing an integral

I am trying to solve

$$ 0 = - \partial_a F(a)-e(a)F(a) + \int_0^{a} e(a')\partial_a F(a') d a' + n $$

optimally, without specifying e(a). But if necessary (as I guess), e(a) = k1exp(k2a). Here's my code:

var('a b k_1 k_2 n')
e(b) = k_1*exp(b*k_2)
F  = function('F', a)
g(b) = e(b)*diff(F,b,1)
de = -diff(F, a, 1) - e(a)*F(a) + g(b).integral(b, 0, a) + n
y = desolve(de, F, ivar=a); y

And the output is

(_C + n*Ei(k_1*e^(a*k_2)/k_2)/k_2)*e^(-k_1*e^(a*k_2)/k_2)

However, I believe that something is wrong with my integral, it is not doing what I expect it to do. For example, if I change the integration boundary to 1:

    de = -diff(F, a, 1) - e(a)*F(a) + g(b).integral(b, 0, a) + n

I will still get the same result:

(_C + n*Ei(k_1*e^(a*k_2)/k_2)/k_2)*e^(-k_1*e^(a*k_2)/k_2)

Where am I going wrong?

2015-05-14 23:24:52 -0500 received badge  Student (source)
2015-05-13 09:45:32 -0500 received badge  Editor (source)
2015-05-13 09:41:29 -0500 asked a question Solve DE with secondary function

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