Bernoulli equation and substitution z = y^{1-n} (Dividebyy^n,setz=y^{1-n}sodz/dx=(1-n))

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Divide by y^n, set z = y^{1-n} so dz/dx = (1-n) y^{-n} dy/dx; equation becomes linear in z.

What each symbol means

SymbolWhat it stands for
nReal exponent (n ≠ 1 for nontrivial reduction; n=0,1 are already linear).

When to use this

Avoid y=0 branch issues when dividing; check singular solutions.