# Math 221e module 2 2nd edition protected

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Module 2 1st Order Differential Equation Techniques (Part 1) DIFFERENTIAL EQUATION Engr. Renel M Alucilja, RPABE Engr. Kathleen Mae B. Alucilja, CE Developed by: COLLEGE OF ENGINEERING AND INFORMATION TECHNOLOGY University of Southern Mindanao Kabacan, Cotabatao 2 Math 221: 1st Order Techniques (Part 1) ================================= Module 2. 1st Order Differential Equation Techniques (Part 1) Learning Outcomes: ILO 4 Solve First Ordinary Differential Equation using Separation techniques ILO 5 Solve First Ordinary Differential Equation using Substitution ILO 6 Solve Linear Differential Equation in order 1 Topics 2. Concept of Mathematical Modeling and Differential Equation 1. Separation of Variable 2. Substitution Methods 1. Homogeneous Equations 2. Linear Equation 3. First Order Linear Equation (Lagrange Equation) 2.1 Separable Differential Equation A differential equation in the first order differential equation is said to be a separable equation if first order differential equation in the form of P( x, y) dx+ Q( x, y) dy=0 can be transformed into Mdx +Ndy=0 where M is a function of x alone and N is a function of y alone. In example, evaluate the differential e siny dx+cos y dy =0 if it is separable or not. equation x Evaluating the equation, we can separate the variable x with variable y following the solution shown below. Example 2.1 x e siny dx +cos y dy =0 1 [ e x siny dx+cos y dy ]=0 1 sin y sin y cos y x e dx+ dy=0 sin y e x dx+ cot y dy =0 [ ] ...
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