Question: numeric calculation

Hi!

I have one equation consists of "x" and "y(x)". This equation does not have any analytic solution, but I found a numeric solution by using "implisitplot". But, apparently this solution is not very good because if I want to plot anything which is related to either itself or its derivatives such as:

a(x) := y(x) + 1

or

b(x) := diff(y(x), x) + 1

I don't have any good result. What shall I do? Can you help me, please?    

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