Bernoulli Differential Equation

Definition

An ODE is called a Bernoulli Differential equation if it can be represented in the form

$$y^{\prime }+a(t)y=p(t)y^{\mathbf{n}}$$ $$\text{ODE}=\{\begin{array}{ll}\text{linear,}& \text{if}n=0\\ \text{linear, }y\text{ can be moved to LHS}& \text{if}n=1\\ \text{non-linear, }n\in \mathbb{R},y\ne 0& \text{if}n>1\end{array}$$

Solution Method

Note: Calculate $u^{\prime }$ with RHS the way it is. Bringing it to LHS makes it less clean.