Simple SDE

**Mathstud28** · April 21st 2008, 01:49 PM

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?

**mr fantastic** · April 21st 2008, 04:49 PM

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 $y \cdot {dy} = x \cdot{dx}$ "...

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