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Introduction to Differential Equations: Slope Fields and Solutions

This resource covers the fundamentals of differential equations, particularly focusing on slope fields and separable equations. It explains how to create a slope field, match equations to the slope field, and sketch graphs based on given initial conditions. Examples include generating slope fields for specific equations, applying separation of variables to solve them, and finding particular solutions using initial conditions. This foundational knowledge equips students with the necessary skills to tackle various problems in differential equations effectively.

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Introduction to Differential Equations: Slope Fields and Solutions

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  1. 6.1 – 6.3 Differential Equations

  2. Differential Equation: An equation which has terms that could include the function (y) and its derivatives (dy/dx or y). Solution equation: y or f (x)

  3. Need to: • Create a slope field • Match y OR dy/dx to the slope field

  4. Ex 1: Create a slope field for the differential equation:

  5. Need to: • Sketch the function (y) given the slope field and an initial condition • Find y using separation of variables

  6. Seperable Differential Equations

  7. Ex 2: Find the solution equation for the differential equation:

  8. Ex 3: Find the particular solution equation for the differential equation given the initial condition f (1) = 1:

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