This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View Full
Document
 Spring '07
 Anoymous
 Differential Equations, Calculus, Equations

Click to edit the document details