Differential Equations: Intro and Direction Fields

Find the derivative of $y$ with respect to $x$.

Draw the slope field for the differential equation $y' = 2y + 3$ and analyze how the slopes change as the value of $y$ changes.

Build a slope field for a given differential equation, using sample points such as (0, 0) and (1, 1) to plot the slopes.

Using a slope field, sketch the solution to a differential equation that passes through a specific point, such as (0, -1).

Find the solution curves by drawing the slope field for the differential equation $\frac{dy}{dx} = x - y$.

Given the differential equation $x^2 + y^2 - 2 = 0$, determine the locations in the graph where the slope ($\frac{dy}{dx}$) is zero, positive, and negative.

Sketch a slope field for $y' = 2xy$ at the indicated points and sketch a solution that passes through (1, 1).

Consider the differential equation $\frac{dy}{dx} = \frac{1}{2}x + y - 1$. Part (a) on the axis provided sketch a slope field for the given differential equation at the nine points indicated.

If I give you the slope field for this differential equation and you want to find a particular solution that goes through the point (0, 2), sketch the solution by following the arrows in the slope field.

Identify the slope field given specific points and determine which letter corresponds to the correct slope field.

Match the differential equation to its slope field given the options: some equations contain only $x$, some contain only $y$, and some contain both $x$ and $y$.