solving a first order differential equation using separation of variables
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/(y^3/2) = dx
integrate both sides to get....
-2*y^(-1/2)= x + C
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.