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

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    No you would get the same answer – 2017-02-25
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    Have you tried doing both substitutions? – 2017-02-25
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    @mrnovice Thanks – 2017-02-26
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    You may recall that one thing that is proved very early on in any ODE course is that for appropriate boundary conditions, solutions are unique. It doesn't matter what tricks you use to get a solution. If you did it right, the answer you get will be the same. – 2017-02-26

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