What to use when reverse chain rule doesnt work?

*highc1157*

Hi there,

My equation to solve is (xy+(x^2))dx + (-1)dy=0

For method of exact solutions, the partials are not equal to each other so I cannot use
exact solutions (reverse chain rule)

I dont know how to solve this

lurflurf

What is reverse chain rule?
Any equation is exact in some coordinates so find them.
you stated (correctly)
(xy+x²)_y - (-1)_x
is not zero but we can use the fact that
(((xy+x²)_y -(-1)_x)/(-1))_y=0
to conclude that the equation is exact in
∫((xy+x²)_y - (-1)_x)/(-1)∂x
and y since (xy+(x²))dx + (-1)dy can be written
(-y-sqrt(-2(-x²/2)))d(-x²/2)-dy

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highc1157	What to use when reverse chain rule doesnt work? Tweet Hi there, My equation to solve is (xy+(x^2))dx + (-1)dy=0 For method of exact solutions, the partials are not equal to each other so I cannot use exact solutions (reverse chain rule) I dont know how to solve this

lurflurf Recognitions: Homework Help	What is reverse chain rule? Any equation is exact in some coordinates so find them. you stated (correctly) (xy+x²)_y - (-1)_x is not zero but we can use the fact that (((xy+x²)_y -(-1)_x)/(-1))_y=0 to conclude that the equation is exact in ∫((xy+x²)_y - (-1)_x)/(-1)∂x and y since (xy+(x²))dx + (-1)dy can be written (-y-sqrt(-2(-x²/2)))d(-x²/2)-dy