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Math Help - integrating factor

  1. #1
    Member
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    integrating factor

    Hello
    The integrating actor of the diferential eqn
    2cos(y^2)dx - xysin(y^2) dy = 0 is
    a) e^x
    b) e^(-x)
    c) 3x
    d) x^3

    Writing in terms of dx/dy I got the anwer to be (cos(y^2))^(1/4). its not even one of the options

    But in terms of dy/dx I dont know what the answer is
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Suppose we want to find an integrating factor only dependent of x, then let M(x,y)=2\cos y^2 and N(x,y)=-xy\sin y^2 and see that \frac1N\left(\frac{\partial M}{\partial y}-\frac{\partial N}{\partial x}\right)=\frac3x, thus u(x)=\exp\left(\int\frac3x\,dx\right)=x^3 is the integrating factor we want.
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