# Math Help - Simple SDE

1. ## Simple SDE

I was reading a book for reviewing the GRE for mathematics...and I came across this problem "Describe the family of curves described by $x\cdot{dy}=y\cdot{dx}$"...so I preceeded to go $\frac{dy}{y}=\frac{dx}{x}$...which means that $ln|y|=ln|x|+C$ which means that $y=Cx$...so I picked choice A" The set of lines intersecting the origin"...but that was incorrect..the asnwer was the set of all circles with center (0,0)...could someone explain?

2. Originally Posted by Mathstud28
I was reading a book for reviewing the GRE for mathematics...and I came across this problem "Describe the family of curves described by $x\cdot{dy}=y\cdot{dx}$"...so I preceeded to go $\frac{dy}{y}=\frac{dx}{x}$...which means that $ln|y|=ln|x|+C$ which means that $y=Cx$...so I picked choice A" The set of lines intersecting the origin"...but that was incorrect..the asnwer was the set of all circles with center (0,0)...could someone explain?
Obviously a typo. The question was probably meant to be

"Describe the family of curves described by $y \cdot {dy} = x \cdot{dx}$"...