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sec9_3 - 9.3 Separable Equations 1 Separable Differentiable...

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9.3 Separable Equations 1. Separable Differentiable Equations Definition 1.1. A differentiable equation is an equation that involves an unknown function and one or more of its derivatives. Definition 1.2. The order of a differentiable equation is the highest derivative in the equation Definition 1.3. A solution for the differentiable equation is a function that satisfies the differentiable equation Definition 1.4. A separable equation is a first-order differentiable equation in which the expression for dy dx can be factored as a function of x times a function of y . In other words, it can be written in the form dy dx = g ( x ) f ( y ) Example 1.1 (Example 1 on p.581) . Solve dy dx = x 2 y 2 . Example 1.2. Find the solution for the above differentiable equation that satisfies

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