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sketch the slope field and some representative solution curves for the given differential equation y′ =x+y...

sketch the slope field and some representative solution curves for the given differential equation y′ =x+y

Please explain I would like to understand the concept please not just the answer.

per the solution book, I dont understand why the solution after the table uts y=-x+1 and after fiferentiate how is the answer 1+x+y and why do we integrate at the end
thank you!

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