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Math Help - Serparable Differential Equation Question

  1. #1
    s3a
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    Serparable Differential Equation Question

    Question:
    Find if satisfies
    and the -intercept of the curve is .
    ?

    My work:
    dy/dx = 12yx^3, y(0) = 6
    integral 1/(12y) dy = integral x^3 dx
    1/12 * ln|y| = e^(1/4 * x^4) + C
    y^(1/12) = e^(1/4 * x^4) + C
    y = e^(3x^4) + C
    6 = e^0 + C
    C = 5
    y = e^(3x^4) + 5

    What am I doing wrong?

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
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     \int \frac{dy}{y} =  \int 12x^{3} dx

     ln y =3x^{4}

     y = e^{3x^{4}} + C \

     6 = e^{3(0)^{4}} + C

    6 = C

     y = e^{3x^{4}} + 6
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  3. #3
    s3a
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    you did what I did but C = 5 not 6 becase 6 - e^0 = C --> C = 6 - 1 = 5
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