Check if you can rewrite it as f(x)dx = g(y)dy — that's separable. For homogeneous, see if it can become dy/dx = F(y/x) alone. I had to revisit this while modelling sound wave decay for my dhol's acoustics. Honestly, the textbook distinction felt neat, but in my messy simulation, the equations often resisted such a clean split — life’s variables are seldom fully separable.
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