How to enter and solve this differential equation?
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])