Thread:

1. Find an equation of the curve.

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

2. 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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