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Math Help - Find an equation of the curve.

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    Find an equation of the curve.

    Find an equation of the curve that satisfies dy/dx=8x^7y and whose y-intercept is 6.
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    Quote Originally Posted by asnxbbyx113 View Post
    Find an equation of the curve that satisfies dy/dx=8x^7y and whose y-intercept is 6.
    The function evaluated at x=0 implies that y=6. Thus, y(0)=6.

    y' = 8x^7 y note y\not = 0,

     \frac{y'}{y} = 8x^7

    \int \frac{y'}{y} dx = \int 8x^7dx

    \ln |y| = x^8 + C

    y = Ce^{x^8} \mbox{ where }C>0

    In order to satisfy the IVP we need C=6.
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