Is it ok to get different solutions if I use different substitutions? (Homogenous ODE)

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Is it possible to get different correct solutions to a Homogenous 1st ODE?

Would substituting different values into an equation give different answers.

ex: $$ -y dx + (x+ \sqrt{ xy})dy = 0$$

possible substitutions could be ...

$$u = \frac{y}{x} $$ or $$u = \frac{x}{y} $$