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    The equation is:

    dy/dx = 2xy - 4xy^2

    I need to solve using the substitution y=1/z

    I found that dy/dx = (-1/z^2)*(dz/dx)

    Therefore after the substitution I ended up with:

    (-1/z^2)(dz/dz) = 2x(1/z) - 4x(1/z^2)

    I was then asked to solve by integrating factor:

    I rearranged into standard form:

    (1/z^2)(dz/dz) * 2x(1/z) = 4x(1/z^2)

    I got the integrating factor to be e^x.

    I ended up with:
    (e^x)(z) = Integral [(e^x)(4x)(1/z^2)]

    How can I integrate the left hand side of the equation if it had z's in it, should i convert back to y at this point?

    Thanks!
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    You've got the substitution right, couple of things I can see though:

    (Original post by _paul)

    I rearranged into standard form:

    (1/z^2)(dz/dz) * 2x(1/z) = 4x(1/z^2)

    Thanks!
    Did you mean dz/dx here?

    (Original post by _paul)

    I rearranged into standard form:

    (1/z^2)(dz/dz) * 2x(1/z) = 4x(1/z^2)

    I got the integrating factor to be e^x.

    I ended up with:
    (e^x)(z) = Integral [(e^x)(4x)(1/z^2)]
    After multiplying everything by z^2 on your standard form bit, I get:

    dz/dx + 2xz = 4x

    Which should give an integrating factor of e^(x^2), I'm not sure where the z has came from in your integral at the end, it should just be the function of x * your integrating factor that you're integrating.

    Hope this helps, ask some more if you need a bit more help.
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    (Original post by _paul)
    The equation is:

    dy/dx = 2xy - 4xy^2

    I need to solve using the substitution y=1/z

    I found that dy/dx = (-1/z^2)*(dz/dx)

    Therefore after the substitution I ended up with:

    (-1/z^2)(dz/dz) = 2x(1/z) - 4x(1/z^2)

    I was then asked to solve by integrating factor:

    I rearranged into standard form:

    (1/z^2)(dz/dz) * 2x(1/z) = 4x(1/z^2)


    I got the integrating factor to be e^x.

    I ended up with:
    (e^x)(z) = Integral [(e^x)(4x)(1/z^2)]

    How can I integrate the left hand side of the equation if it had z's in it, should i convert back to y at this point?

    Thanks!
    I assume that the first bolded is supposed to be an x.

    The second bolded isn't in standard form. It is also incorrect.
 
 
 
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