So I understand that I need to take the derivative of y and plug that in, but do

Question

So I understand that I need to take the derivative of y  and plug that in, but do I also need to solve for x too? Or am I overthinking this

In Problems 15-18 verify that the indicated function y = phi(x) is an explicit solution of the given first-orde differential equation. Proceed as in Example 2, by considering phi simply as a function, give its domain. Then by considering phi as a solution of the differential equation, give at least one interval I of definition (y - x)y' = y - x + 8; y = x + 4

Explanation / Answer

I think you are absolutely right. You only need to solve for y and no need to solve for x.

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