Question

Find an equation of the curve through (1,1) the slope of whose tangent line at (x,y) is y^9x^6.
Express your answer as y^-8=

Answer 1

The wording is a bit different but think of it as just a differential equations problem:
dy/dx=y^9x^6 and y(1)=1

Answer 2

So after I separate and integrate each side I should get -1/8y^8=(-1/5x^5)+C right?

Answer 3

Looks like basic algebra to me.