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If it is any help, $ y = \sqrt{2} (k-x^2)^{1/2}$ is the$ y = \pm \sqrt{2} (k-x^2)^{1/2}$ are homogeneous solutionsolutions, that is, it solvesthey solve$$y^\prime + \dfrac{2x}{y} = 0$$
If it is any help, $ y = \sqrt{2} (k-x^2)^{1/2}$ is the homogeneous solution, that is, it solves$$y^\prime + \dfrac{2x}{y} = 0$$
If it is any help, $ y = \pm \sqrt{2} (k-x^2)^{1/2}$ are homogeneous solutions, that is, they solve$$y^\prime + \dfrac{2x}{y} = 0$$
