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Thread: 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 $\displaystyle x=0$ implies that $\displaystyle y=6$. Thus, $\displaystyle y(0)=6$.

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

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

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

    $\displaystyle \ln |y| = x^8 + C$

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

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