Solve the first-order separable equationh(y) dydx = g(x)by completing the following

Chapter 8, Problem 1

(choose chapter or problem)

Solve the first-order separable equation

                                                              \(h(y) \frac{d y}{d x}=g(x)\)

by completing the following steps:

Step 1 . Separate the variables by writing the equation in the differential form________.

Step 2 . Integrate both sides of the equation in Step 1 : ________.

Step 3. If \(H(y)\) is any antiderivative of \(h(y), G(x)\) is any antiderivative of \(g(x)\), and \(C\) is an unspecified constant, then, as suggested by Step 2 , the equation ________ will generally define a family of solutions to \(h(y) d y / d x=g(x)\) implicitly.

Equation Transcription:

Text Transcription:

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

H(y)

h(y), G(x)

g(x)

C

h(y) dy/dx = g(x)