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    Exact equations

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    First determine if the equation is exact. If it is exact, find the general solution, or at least a relation that defines the solutions implicitly:
    [cos(x^2 + y) - 3xy^2]y' + 2x cos(x^2 + y) - y^3=0

    © BrainMass Inc. brainmass.com February 24, 2021, 2:19 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/exact-equations-implicit-differentiation-13774

    Solution Preview

    To find whether it is exact or not we shall rewrite it as:

    [cos(x^2 + y) - 3xy^2]dy+[2x cos(x^2 + y) - y^3]dx=0

    Then
    p(x,y)=2x cos(x^2 + y) - y^3
    Q(x,y)=cos(x^2 + y) - 3xy^2

    The derivative of P wrt y would ...

    Solution Summary

    This shows how to find if an equation is exact. The implicit differentiation is provided.

    $2.19

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