I was reading a book for reviewing the GRE for mathematics...and I came across this problem "Describe the family of curves described by $\displaystyle x\cdot{dy}=y\cdot{dx}$"...so I preceeded to go $\displaystyle \frac{dy}{y}=\frac{dx}{x}$...which means that $\displaystyle ln|y|=ln|x|+C$ which means that $\displaystyle y=Cx$...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?
I was reading a book for reviewing the GRE for mathematics...and I came across this problem "Describe the family of curves described by $\displaystyle x\cdot{dy}=y\cdot{dx}$"...so I preceeded to go $\displaystyle \frac{dy}{y}=\frac{dx}{x}$...which means that $\displaystyle ln|y|=ln|x|+C$ which means that $\displaystyle y=Cx$...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?
"Describe the family of curves described by $\displaystyle y \cdot {dy} = x \cdot{dx}$"...