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Math Help - separable equation

  1. #1
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    separable equation

    Find particular solution of the separable equation

    6(x^4-3x)dx+\frac{1}{y^3}dy=0
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  2. #2
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    ok, so now I have some idea how this LATEX works, I will try to post my attempted solution
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  3. #3
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    Sorry,it's obvious that I haven't got to grips with Latex
    Last edited by redskies; August 10th 2010 at 09:53 AM. Reason: image too big
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  4. #4
    Super Member 11rdc11's Avatar
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    (6x^4-18x)dx=(-y^{-3})dy

    \int(6x^4-18x)dx=-\int(y^{-3})dy

    \frac{6}{5}x^5-9x^2+c=-\frac{-y^-2}{-2}

    \frac{6}{5}x^5-9x^2+c=\frac{1}{2y^2}

    Looks right except for that you need a 2 on the final step
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  5. #5
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    I forgot to say that at the beginning I am told that y(0)=1

    I will try to show my solution later.Sorry for being a nuisance.
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  6. #6
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    (6x^4-18x)dx=(-y^-3)dy

    \int(6x^4-18x)dx=\int(-y^-3)dy

    \frac{6}{5}x^5-9x^2+c=\frac{1}{2y^2}

    y(0)=1

    \frac{6}{5}(0)^5-9(0)^2+c=\frac{1}{2(1)^2}

    c=\frac{1}{2}

    Now I have:

    \frac{6}{5}x^5-9x^2+\frac{1}{2}=\frac{1}{2y^2}
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  7. #7
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    Should I stop there, or proceed to express it as y=

    like this:
    multiplying across by 10 , I get:

    12x^5-90x^2+5=\frac{5}{y^2}

    Therfore:

    y^2(12x^5-90x^2+5)=5

    y=\frac{\sqrt5}{\sqrt(12x^5-90x^2+5)}
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  8. #8
    Super Member 11rdc11's Avatar
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    looks good.
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