Chapter 6.1, Problem 27E

To determine

To choose: The correct graph that match the given differential equation.

Answer to Problem 27E

The correct option is (a)

  

Explanation of Solution

Given information:

The differential equation is: $\frac{dy}{dx}={(\cos x)}^2$

Calculation:

The given differential equation is: $\frac{dy}{dx}={(\cos x)}^2$

Since a square is always a positive number thanks to the even power of $\cos x$ , the slope is always positive. As a result, since (c) and (d) have negative slopes for some values of $x$ they are no longer viable options.

Hence

  $\begin{array}{c}$ {(\cos 0)}^2=1^2$=1\end{array}$

Since (b) has a slope of 0 at the origin, it can't be an answer because the slope at the origin must be 1. The appropriate response is therefore (a).

The required correct option is (a) that match the given differential equation.