3.3.16 Bernoulli ode \(y^{\prime }+Py=Qy^{n}\)

ode internal name "bernoulli"

This has the form \(y^{\prime }+Py=Qy^{n}\) where \(n\neq 1,n\neq 0\). Solved by dividing by \(y^{n}\) and then using the substitution \(v=y^{1-n}\). This converts the ode to linear ode \(v^{\prime }+\left ( 1-n\right ) Pv=\left ( 1-n\right ) Q\) which is solved for \(v\), then \(y\) is found.