Mr. Integral
Math notes/Differential Equations/First-Order Methods

Bernoulli Equations and Substitutions — Cheat sheet

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Core rule

v=y1−n  ⟹  v′+(1−n)pv=(1−n)q.v=y^{1-n}\implies v'+(1-n)pv=(1-n)q.

Watch for

The inverse substitution can introduce branch restrictions or a finite-time singularity. A linear transformed solution need not correspond to a real original solution on its entire interval.