What to use when reverse chain rule doesnt work?

  • Thread starter highc1157
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  • #1
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Main Question or Discussion Point

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
 

Answers and Replies

  • #2
lurflurf
Homework Helper
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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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