Bernoulli Differential Equation

A Bernoulli Differential equation is defined by the form

$$\frac{dy}{dx}+P(x)y=Q(x)y^n$$

• If $n=0$ the equation becomes linear

Solving a Bernoulli Differential Equation

With the substitution $u=y^{1-n}$ the equation can be transformed to the linear equation

\frac{du}{dx} + (1-n)P(x)u=(1-n)Q(x)$$ This equation can be solved using methods for [[First Order Differential Equations|linear differential equations]]