If it is any help, $ y = \sqrt{2} (k-x^2)^{1/2}$ is the homogeneous solution, that is, it solves $$y^\prime + \dfrac{2x}{y} = 0$$
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anon
If it is any help, $ y = \sqrt{2} (k-x^2)^{1/2}$ is the homogeneous solution, that is, it solves $$y^\prime + \dfrac{2x}{y} = 0$$