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Thread: dy/dx = 12yx^3

  1. #1
    s3a
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    dy/dx = 12yx^3

    The question is:
    dy/dx = 12yx^3, y(0) = 6

    My work:
    (My work is attached) but here is the final answer I get y = 5e^(3x^4) which is supposedly wrong.

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by s3a View Post
    The question is:
    dy/dx = 12yx^3, y(0) = 6

    My work:
    (My work is attached) but here is the final answer I get y = 5e^(3x^4) which is supposedly wrong.

    Any help would be greatly appreciated!
    Thanks in advance!
    Separate the variables

    $\displaystyle \frac{dy}{y} = 12x^3\,dx$

    $\displaystyle \ln |y| = 3x^4 + C$

    $\displaystyle |y| = e^{3x^4+C} = Ae^{3x^4} \text{ where } A = e^C$

    Initial condition: (0,6)

    $\displaystyle 6 = Ae^0 \: \rightarrow \: A = 6$

    Therefore the equation is $\displaystyle |y| = 6e^{3x^4}$
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