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**6.4 day 1 Separable Differential Equations**

Jefferson Memorial, Washington DC Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2007

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A separable differential equation can be expressed as the product of a function of x and a function of y. Example: Multiply both sides by dx and divide both sides by y2 to separate the variables. (Assume y2 is never zero.)

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**Separable Differential Equations**

A separable differential equation can be expressed as the product of a function of x and a function of y. Example: Combined constants of integration

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Example: Separable differential equation Combined constants of integration

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**p Example: We now have y as an implicit function of x.**

We can find y as an explicit function of x by taking the tangent of both sides. Notice that we can not factor out the constant C, because the distributive property does not work with tangent. p

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3.3 Rules for Differentiation Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003 The “Coke Ovens”,

3.3 Rules for Differentiation Colorado National Monument Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003 The “Coke Ovens”,

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