Separable first-order equation (If dy/dx factors as a function of x times a function of y, separate and)

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If dy/dx factors as a function of x times a function of y, separate and integrate both sides; add one constant of integration.

What each symbol means

SymbolWhat it stands for
g(x)Function of x only.
h(y)Function of y only (watch zeros where separation invalid).

When to use this

h(y) ≠ 0 in the interval (or handle h(y)=0 as singular solutions separately).