Answer to Question #26104 in Differential Equations for Adam

Question #26104
Given an ODE, let x: I -> R^n be a solution defined on an interval I, a subset of R. A phase curve in R^n is the image x(I) where x is a solution to the ordinary differential equation. Consider the ODE: dx/dt = x dy/dt = ky (1) where k is a constant. Giving a detailed answer: Is the curve give by |y| = C|x|^k where C is a constant, a phase curve of the ODE (1)?
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