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What to use when reverse chain rule doesnt work?

  1. Oct 28, 2011 #1
    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
     
  2. jcsd
  3. Oct 29, 2011 #2

    lurflurf

    User Avatar
    Homework Helper

    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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