CHAPTER 2 - EQUATION OF ORDER ONE

CHAPTER 2 - EQUATION OF ORDER ONE

1. METHOD 2.8 : COEFFICIENTS LINEAR IN TWO VARIIABLE

   • 2. parallel / does not intersect
   • 1. intersect

2. METHOD 2.2 : HOMOGENOUS COEFFICIENT

   • THEOREM 1 : IF M(X,Y) AND N(X,Y) ARE BOTH HOMOGENOUS AND SAME DEGREE, THE FUNCTION M(X,Y) / N(X,Y) IS HOMOGENOUS OF DEGREE ZERO
   • THEOREM 2 : IF F(X,Y) IS HOMOGENOUS OF DEGREE ZERO IN X AND Y, F(X,Y) IS A FUNCTION OF Y/X ALONE

3. METHOD 2.1 : SEPARATION OF VARIABLES

   • 1. separate the variable of x and y from the given differential equation
   • 2. find the general solution by integration both sides
   • 3. obtain c for particular solution

4. METHOD 2.3 : EXACT EQUATION

   • 1. test of exactness : dM/dy = dN/dx
   • 2. integrate the equation according to the easiest one either M or N
   • 3. if M is chosen, then differentiate M respect to Y. if N, differentiate respect to x. compare with the original equation to find g

5. METHOD 2.4 : INTEGRATING FACTOR

   • 1. formed the equation into linear formed
   • 2. find the integrating factor
   • 3. multiply the integrating factor with the original linear equation

6. METHOD 2.7 : BERNOULLI'S EQUATION

   • 1. non-linear equation that need to convert into the linear equation by making a change of the dependent variable that convert it into linear equation.
   • 2. followed by integrating factor

7. METHOD 2.6 : SUBSTITUTION

   • 1. the equation cannot be solve by ather method
   • 2, substitute variable with another variable for easiest way

8. METHOD 2.5 : DETERMINATION OF INTEGRATING FACTOR