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Math Help - Simple SDE

  1. #1
    MHF Contributor Mathstud28's Avatar
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    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?
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    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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