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I want to solve : $y'(x)=y(x+1)$ ! I don't know how to solve it ! form what tried I know that y must be nonlinear function also it can't be polynomial! if we replace the 1 with $\frac{\pi}{2}$ then $y=sin(x)$ must satisfy the equation ! if : $y'(x)=\frac {y(x+1)}{e}$ then $y=e^x$ is a solution , so how we solve these equations ?

Fayez Abdlrazaq Deab
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    These type of equations are called Delay Differential Equations, they are specific branch of ODE. So at first try to search for analytical methods on how to solve these type of equations – Tomas May 29 '13 at 10:36
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    @Tomas, I wouldn't classify DDEs as ODEs; however, they are certainly more difficult to solve than ODEs. – J. M. ain't a mathematician May 29 '13 at 10:38
  • Yeah, you are right. I too quickly jumped to conclusions. – Tomas May 29 '13 at 10:42
  • Laplace transforms will likely be of use. They "undo" both differentiation and shifting. – abnry May 29 '13 at 11:27
  • I will suggest you look at the question/answers of a similar delayed differential equation here. – achille hui May 29 '13 at 11:58
  • This is not quite the same equation as for the Dickman function, but maybe the discussion of that function at http://en.wikipedia.org/wiki/Dickman_function and elsewhere could give you some ideas. – Gerry Myerson May 29 '13 at 12:42

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