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Unformatted text preview: Friday January 28 Lecture 11 : Separable Differential equations . (Refers to Section 9.3 in your text) Expectations: 1. Recognize a separable differential equation. 2. Solve a separable differential equation. We will study two types of differential equations for which we have clear methods of solution. 11.1 Definition A first order differential equation which can be written in the form is called a separable differential equation . 11.2 Theorem Suppose a differential equation can be written in the form N ( y ) dy = M ( x ) dx where y varies as a function of x . Then Hence its complete solution (possibly an implicit solution ) can be found by integrating both sides of the DE with respect to their own variables. Proof: Suppose we are given that N ( y ) dy = M ( x ) dx and y = y ( x ). - Suppose that the function H represents an antiderivative of the function N . 11.3 Example Find a function y = f ( x ) which is a solution to the initial value problem We express the differential equation as...
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