Question

I need help with an implicit function.

Answer 1

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.

Answer 2

without knowing what y(x) looks like, the best we can say is the equation is true for y(0)=0

Answer 3

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?

Answer 4

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?

Answer 5

Ah, I see. All the other possibilities are ruled out because otherwise the last equation would make no sense.

Answer 6

Thank you ZeHanz for your help.

Answer 7

yw!