Chapter 9, Problem 1GYR

To determine

The first-order differential equation and also when a function is the solution of such equation.

Explanation of Solution

A first-order differential equation is of the form $\frac{dy}{dx}=f\left(x,y\right)$ in which $f\left(x,y\right)$ is a function of two variables defined on a region in the xy-plane.

Since the equation involves only the first derivative $\frac{dy}{dx}$, it is called first-order differential equation.

A function $y\left(x\right)$ is said to be the solution of the differential equation, when $y\left(x\right)$ and its derivative are substituted in the differential equation, the resulting equation must be true.

The general solution always contains an arbitrary constant and it contains all the possible solutions.