First order differential equations
                                                         Samy Tindel
                                                         Purdue University
                      Differential equations and linear algebra - MA 262
                     Taken from Differential equations and linear algebra
                                                  Pearson Collections
                   Samy T.                                     First order                        Differential equations      1 / 40
    Outline
     1    Separable equations
     2    Linear equations
     3    Exact equations
     4    Change of variables
     5    Chapter review
                   Samy T.                                     First order                        Differential equations      2 / 40
    Outline
     1    Separable equations
     2    Linear equations
     3    Exact equations
     4    Change of variables
     5    Chapter review
                   Samy T.                                     First order                        Differential equations      3 / 40
    General form of separable equation
     General form of first order differential equation:
                                                         y′ = f (x,y)
            Definition 1.
           A first order separable differential equation is of the form
                            h(y)dy = g(x)                    ⇐⇒ h(y)dy =g(x)dx                                         (1)
                                    dx
     Solving separable equations:
     Integrate on both sides of (1).
                   Samy T.                                     First order                        Differential equations      4 / 40