The Bernoulli Equation // Substitutions in Differential Equations
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The Bernoulli Equation is a fascinating ODE. On the surface it is a non-linear first order ODE which means we can't use the methods we have developed for first order linear differential equations. However, with a substitution u=y^(1-n), this converts into a linear ODE and then we can use the method of integrating factors. There are a lot of little substitution tricks like this one in ODEs, and we won't do most of them, but the big idea is to be always looking for ways you can convert an ODE you don't know into one you can do.
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