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I am knew to this site. Hopefully It will end my search.

Let us take a non-linear IVP $dy/dx = (1-2x) y^2$ with $y(0) = y_0$

Now my questions are: (A) Show that this initial value problem has a unique solution for any choice of $y_0$ and (B) How does the interval of definition of the solution depend on $y_0$ ?

Could you explain the procedure to answer those questions? please...

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    For question (A), look in your notes or textbook for a general existence and uniqueness theorem. It will cover this case. Check all assumptions and apply it. For (B), solve the equation. HINT: The right hand side is already factored.2012-03-06

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