what is the solution to the differential equation dy/dx=y^2, where y(-1)=1?

Answer 1

dy/dx = y²

Using separation of variables:

∫dy/y² = ∫dx

-1/y = x + C --> y = -1/(x+C)

At (-1,1)

1 = -1/(-1 +C) --> C = 0

y = -1/x