Chapter 8.2, Problem 1QCE

Solve the first-order separable equation

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

by completing the following steps:

Step 1. Separate the variables by writing the equation in the differential form $\text{\_\_\_\_\_}\text{.}$

Step 2. Integrate both Sides of the equation in Step 1: $\text{\_\_\_\_\_}\text{.}$

Step 3. If $H\left(y\right)$ is any antiderivative of $h(y),G(x)$ is any antiderivative of $g\left(x\right),$ and $C$ is an unspecified constant, then, as suggested by Step 2, the equation $\text{\_\_\_\_\_}$ will generally define a family of solutions to $h(y)dy/dx=g(x)\text{implicitly}\text{.}$