§7.4 Separable differential equations

Introduction

In this preview activity, we explore whether certain differential equations are separable or not, and then revisit some key ideas from earlier work in integral calculus.

Which of the following differential equations are separable? If the equation is separable, write the equation in the revised form $g(y) \frac{dy}{dt} = h(t)$.

-$\displaystyle \frac{dy}{dt} = -3y$. -$\displaystyle \frac{dy}{dt} = ty - y$. -$\displaystyle \frac{dy}{dt} = t + 1$. -$\displaystyle \frac{dy}{dt} = t^2 - y^2$.