What's the solution of : dy/dx=ay^2

Question

With a a constant and y the derivative of Y.

I find

y(x) = y(0)•exp(aY+c)

With c a constant. Thank you for helping.

Answer 1

We solve these equations by having y terms on the dy side and x terms on the x side

dy/y^2 = a dx

Integrating,

-1/y = ax + c

y = -1/(ax + c)

Answer 2

dy/y² = a dx

y^-2 dy = a dx

Integrating

y^-1/ -1 = ax + C

-1/y = ax + C

1/y = -ax - C

y = 1 / (-ax-C) where C is a constant