Slope fields
▶ Introducing slope fields
Slope fields allow us to analyze differential equations graphically. Learn how to draw them and use them to find particular solutions.
▶ Working an example: equation from slope field
Given a slope field and a few differential equations, we can determine which equation corresponds to the slope field by considering specific slopes.
▶ Working an example: slope field from equation
Given a differential equation in x and y, we can draw a segment with dy/dx as slope at any point (x,y). That's the slope field of the equation. See how we match an equation to its slope field by considering the various slopes in the diagram.
▶ Working an example: forming a slope field
Given a differential equation in x and y, we can draw a segment with dy/dx as slope at any point (x,y). That's the slope field of the equation. See how we determine the slopes of a few segments in the slope field of an equation.
▶ Approximating solution curves in slope fields
Given the slope field of a differential equation, we can sketch various solutions to the equation.
▶ Working an example: range of solution curve from slope field
Given the slope field of a differential equation, we can sketch various solutions to the equation. In this example, we analyze the range of a specific solution.
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