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I need help with an implicit function.

Mathematics
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The function can be seen on the picture. I should show that y(0)=0 but I stuck at the step you see on the picture. It seems possible at that step that y(0)=0 is a solution but there still might be others too.
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  • phi
without knowing what y(x) looks like, the best we can say is the equation is true for y(0)=0
I can follow all of your steps. The last one is: \[y(0)=\ln (1-y(0))\]Now consider this: there are three possibilities for y(0): 1. y(0)=0 2. y(0)>0 3. y(0)<0 Can you see where this leads to?

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Suppose y(0) = 0. Because ln(1-0)=ln(1)=0, this works. What about other values instead of 0? Why wouldn't that be possible?
Ah, I see. All the other possibilities are ruled out because otherwise the last equation would make no sense.
Thank you ZeHanz for your help.
yw!

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