How to enter and solve this differential equation?

asked 2012-11-23 14:19:29 +0200

Rob N gravatar image

I'm studying electronics and I've encountered the weird and interesting relationship between the exponential function and the sine and cosine functions. In my effort to understand this better, I'd like to solve the following differential equation.

f'(x) = f(x+1), or more generally...
f'(x) = f(x + k) for any constant k

I wanted to explore these functions because the exponential function is where k = 0 and the sin(x) is solution when k=pi/2. I wanted to see what was "in between" those two. I know how to find the e^x case:

x = var('x')
y = function('y', x)
desolve(diff(y,x) == y, y, [0,1])

but, is there a way to add the k, something like this (which doesn't work as written):

desolve(diff(y,x) == y(x+1), y, [0,1])
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As you certainly know this is not an ordinary different equation. Sometimes the term Delay differentia equation. It seems that desolve does not handle this case. However for a genral 'k' I doubt that there exists any formula. In the aformentioned wikipedia article, there are some numerical approach to these problems...

vdelecroix gravatar imagevdelecroix ( 2016-01-05 03:14:22 +0200 )edit