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OpenStudy (anonymous):
Let x:I -> R^n be a solution defined on an interval I subset of R. Consider the ODE xdot = x ydot = ky where k is a constant. Is the curve given by: |y| = C|x|^k a phase curve of the ODE? (C is a constant. A phase curve in R^n is the image x(I0 where x is a solution to the ODE)
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