Math 224-01: Differential Equations: Reading Homework 1.6

1. Separable Differential Equations : what type of differential equations do we look at solving in this section?
   
   1. Separable Equations : why are these equations called ``separable''?
      
      1. Point : what are the steps in solving a separable ODE?
         
      2. Point : in using this procedure, how are we able to rewrite N(y)y'(x) + M(x) as (G(y(x)) + F(x))'?
         
      3. Point : what is the differential form of an equation?
         
   2. Integrals and Integral Curves : what is the integral of an ODE? what is an integral curve?
      
      1. Point : how are solutions related to integral curves of an ODE?
         
      2. Point : how might we find the largest x-interval on an integral curve for which a solution is defined?
         
   3. Applications : what applications is separation used on? why won't the method of integrating factors work for these?