Bernoulli & Substitution Methods

The Bernoulli equation y′ + P(x)·y = Q(x)·yⁿ has that yⁿ on the right, which breaks linearity for any n ≠ 0, 1. You can't apply the integrating factor directly. But there's a change of variables so clean it feels like cheating: pick the right new variable and the nonlinearity simply evaporates.