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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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