Chapter 6, Problem 10RWDT

To determine

To find: If slope field shows horizontal segments everywhere along the line $y=3$ what you conclude about differential equation.

Answer to Problem 10RWDT

It can be concluded that the differential equation has the solution at $y=3$ .

Explanation of Solution

Given information:

The slope field shows horizontal segments everywhere along the line $y=3$ .

This gives the idea that the slope at $y=3$ is zero.

This can be written as $\frac{dy}{dx}=0$ but in order to solve a differential equation there must be some function at right hand side.

It can be assumed that equation will look like $\frac{dy}{dx}=(y-3)f(x,y)$

If slope is zero at $y=3$ then $\frac{dy}{dx}=(y-3)f(x,y)$ will become:

  $\begin{array}{c}(y-3)f(x,y)=0\\ y-3=0\end{array}$

because $f\left(x,y\right)$ cannot be zero.

It can be concluded that the differential equation has the solution at $y=3$ .