Bernoulli Equation

Used to find the solution to an equation of the standard form,

`y'=F(x)y+G(x)y^2`

Using the substitution,

`w=y^(-1)` and `(dw)/(dy)=-y^(-2)=-w^2`

The equation becomes,

`y'=F(x)w^(-1)+G(x)w^(-2)`

Multiplying the l.h.s by dw/dy, and the right hand side by –w², we obtain a first order differential equation,

`(dw)/(dx)=-F(x)w-G(x)`

Which can be solved using the integrating factor method.

For more information see https://en.wikipedia.org/wiki/Bernoulli_differential_equation