Find an equation of the curve.

**asnxbbyx113** · June 5th 2007, 06:17 PM

Find an equation of the curve that satisfies dy/dx=8x^7y and whose y-intercept is 6.

**ThePerfectHacker** · June 5th 2007, 06:35 PM

Originally Posted by asnxbbyx113

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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