Answer to Question #26104 in Differential Equations for Adam

Question

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)?