Find an equation of the curve that satisfies dy/dx=150yx^14 and whose y-intercept is 6.

Answer 1

My work so far:

dy/dx = 50yx^14
ln(y) = 10yx^15+C
y(0)=6
y=10(6)x^15+C

Help?

Answer 2

dy/dx=150yx^14

divide both sides by y

(dy/dx) / y = 150x^14

ln(y) = 10 x^15 + c

but (0,6) lies on it, so
ln 6 = 10(0) + c
c = ln 6

ln y = 10x^15 + ln 6
is one such equation