this is a rather elementary problem for diff. eq, and i solved it correctly using separation of variables, but there is a reason that the answer y=4/(x^2) is only valid for x<0.

dy/dx=y^(3/2)

dy/(y^3/2) = dx

integrate both sides to get....

-2*y^(-1/2)= x + C

-2=(x+C)*y^(1/2)

y^(1/2) = -2/(x+C)

y = 4/[(x+C)^2]

so...for some reason, when i solved for y explicitly in terms of x, I shold have been able to predict that the solution y = 4/x^2 is only valid for x<0

but I cant figure out what step in my algebra should have led me to conclude that the solution y = 4/x^2 is only valid for x<0.

any help appreciated.