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How to solve differential equations of the following form:

$\frac{df}{dx} = f(x+1)$

Jepsilon
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Fayez Abdlrazaq Deab
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    Not really sure about solving because this isn't my field, but after a quick Google search, these are a specific type of differential equations known as Functional Differential Equations (FDEs) https://en.m.wikipedia.org/wiki/Functional_differential_equation – Jepsilon Jan 11 '19 at 07:50
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    Because I cannor edit my comment: If you work with the assumption that $f$ is linear, i.e. $f(a+b)=f(a)+f(b)$, you can easily solve it normally as $f(x)=Ae^x-f(1)$ and substituting $x=1$ you get $f(1)=\frac{Ae}{2}$. Then you find $A$ with some initial condition. – Jepsilon Jan 11 '19 at 08:06
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    @Jepsilon This is also a delay differential equation whose solutions are well-known – Dylan Jan 11 '19 at 12:49
  • Thank you for your helpful comments – Fayez Abdlrazaq Deab Jan 22 '19 at 03:20

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