Separable DEQs

A first order DE is separable if it can be written in the form

$$\frac{dy}{dx}=g(x)p(y)$$

Solving

1. Check whether zeros of $p(y)$ are solutions of equations
   • Important because sometimes they aren’t included in the general solution you find
   • Finds constant solutions (in the form $y=a$)
2. Divide both sider by $p(y)$ and multiply both sides by $dx$ and reduce it to the form $h(y)dy=g(x)dx\text{ where }h(y)=\frac{1}{p(y)}$
3. Integrate both sides to obtain an implicit solution $H(y)=G(x)+C$