Select from the choices below the slope field for the differential equation. $\frac { d y } { d x } = 2 \sin x$
D) none of the above

Question

Quizplus · Accepted Answer

The slope of a solution curve at any point is given by the value of the derivative at that point. Therefore, the slope field should indicate the value of $\frac{dy}{dx}$ at different points in the plane. For the given differential equation, we have $\frac{dy}{dx} = 2\sin x$. The slope of the solution curve will depend on the value of $\sin x$ at each point, and not on the sign of $\sin x$. Therefore, the slope field should contain identical slopes in the regions where $\sin x$ takes the same value, but with opposite signs in the regions where $\sin x$ changes sign. Choice B satisfies this requirement.

Select from the Choices Below the Slope Field for the Differential