Chapter 7.1, Problem 69E

To determine

To state whether the given statement “Any tow solutions to the differential equation $\frac{dy}{dx}=5$ are parallel lines” is true or false.

Answer to Problem 69E

The given statement “Any tow solutions to the differential equation $\frac{dy}{dx}=5$ are parallel lines” is true.

Explanation of Solution

Given information :

The statement “Any tow solutions to the differential equation $\frac{dy}{dx}=5$ are parallel lines”.

Calculation:

Consider, $\frac{dy}{dx}=5$ .

Integrating both sides,

  $\begin{array}{c}{\displaystyle \int \frac{dy}{dx}}={\displaystyle \int 5}\\ {\displaystyle \int dy}={\displaystyle \int 5dx}\\ y=5x+C\end{array}$

Here the slope is constant. Thus any tow solutions have the constant slope are parallel.