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## Homework Statement

I have the ODE [itex] y' = f(\frac{y}{x}) [/itex], and I want to re-write this as a separable equation using the change of variable [itex] u = \frac{y}{x} [/itex]

## The Attempt at a Solution

I use the chain rule to write [itex] y' = \frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx}

= \frac{dy}{du}(-\frac{y}{x^2}) = -\frac{dy}{du}\frac{u^2}{y} = f(u) [/itex]

which is a separable equation. However this seems to be wrong somehow because when I try using it to solve equations of the above form, I'm getting the wrong answer. Any help where I went wrong?