Chapter 6.1, Problem 26E

To determine

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

Answer to Problem 26E

The correct option is (c)

  

Explanation of Solution

Given information:

The differential equation is: $\frac{dy}{dx}={(\sin x)}^3$

Calculation:

The given differential equation is: $\frac{dy}{dx}={(\sin x)}^3$

  $\sin x$ can be any value from $-1\text{ to }1$ so ${(\sin x)}^3$ can be any value between ${(-1)}^3=-1$ and

  $1^3=1$ .Since (a) and (b) contain only positive slopes, this indicates that the slope alternates between positive and negative values, excluding them from the list of viable replies.

Put $x=0$ gives

  $\begin{array}{c}$ \frac{dy}{dx}={(\sin 0)}^3$=0^3\\ =0\end{array}$

so the slope when $\text{ x=0}$ is 0, removing (d) from the possible answers since this has a positive nonzero slope when $\text{ x=0}$

The sole remaining response option is (c).

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