I was solving a separable differential equation from my textbook and when I got the answer I verified that my answer was in fact a solution of the original D.E. but when I looked at the answer in the book looked a little bit different from mine.
This is the original D.E. :
xy' + y = y^2
This is my answer:
y = c/(c-x)
This is the answer in the book
y = 1/(1-cx); also y=0 and y=1 are singular solutions.
Honestly I still don't know how to check if there are singular solutions, I didn't quite understand the explanation in the book, is it easy, ? And as for the general solution how does y = c/(c-x) become the same as y = 1/(1-cx)?
If I divide numerator and denominator by c then I get y = 1/(1-(x/c)), but is x/c just the same as cx? and if so is this something that applies only when dealing with differential equations?