Question

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)