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In his book on differential equations, Arnold writes that $x'(t)=x(x(t))$ is not a differential equation.

My question is: how can one solve it?

zar
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1 Answers1

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Here is a partial attempt: Let $x=At^n$ then $\displaystyle {nAt^{n-1}=A^{n+1} t^{n^2}}$. From which you get $n^2=n-1$ and $A^{n}=n$ resulting in some complex number answers that would need to be analyzed for being meaningful.

A general solution would be interesting though. The equation reminds me of a "delay differential equation" but with variable unknown delay.

Maesumi
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