Chapter 6: Slope Fields



Chapter 6: Slope Fields and Initial Value Problems

Slope fields: a geometric solution to a differential equation

Creating a slope field:

dy/dx – slope of the tangent line, so using dy/dx find the slope at each point.

Draw a tiny tangent line at each point with it’s appropriate slope

Using a slope field:

Draw a solution to the differential equation by plotting the initial condition, then using the tiny tangent lines as guides, draw the solution curve. You are not connecting the lines.

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Solving Initial Value problems:

Separate variables

Integrate both sides

Find antiderivatives

Substitute initial condition and solve for C

Write equation using value for C

Solve for y

Recognize initial condition

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