Timeline for Reference request: a singular differential equation
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 27, 2018 at 15:39 | comment | added | Alexandre Eremenko | @Bazin: Yes, in this example zero is the unique analytic function which satisfies your equation. The solution is always unique.. | |
| Feb 27, 2018 at 14:27 | comment | added | Bazin | Take $a=1/2$, $f=0$, so that the equation reads $2x z'=z$. Multiplying both sides by $z$, calling $y=z^2$, you get $xy'=y$ and thus $y=\alpha x$. If $z$ is analytic, $:alpha\not=0$,and $\zeta= \alpha^{-1/2}z$, you found an analytic function $\zeta$ such that $\zeta^2=x$, which is not possible. Thus $z=0$. | |
| Feb 27, 2018 at 12:40 | vote | accept | Alex Gavrilov | ||
| Feb 26, 2018 at 23:12 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Feb 26, 2018 at 15:31 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Feb 26, 2018 at 14:22 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |