Check Your Understanding

Draw a slope field for each differential equation. Each tick mark is one unit.

$\frac{dy}{dx}=-y$

$\frac{dy}{dx}=\frac{x}{y}$

Sketch the particular solution to $\frac{dy}{dx}=-y$ that passes through $(0,-1)$ on your slope field above.

The slope field of differential equation is shown below. Which of the following equations could be a specific solution to that differential equation?

A$.$

B$.$

C$.$

D$.$

$y=e^x$

$y=x^2$

$y=lnx$

$y=sinx$