Solving Simple Differential Equations           Separable Variables            Revisiting IVPs and Models            Conclusion
                                                       MATH312
                                Section 2.2: Separable Variables
                                               Prof. Jonathan Duncan
                                                      Walla Walla College
                                                 Spring Quarter, 2007
    Solving Simple Differential Equations           Separable Variables            Revisiting IVPs and Models            Conclusion
    Outline
           1    Solving Simple Differential Equations
           2    Separable Variables
           3    Revisiting IVPs and Models
           4    Conclusion
    Solving Simple Differential Equations           Separable Variables            Revisiting IVPs and Models            Conclusion
    Solving a DE by Integration
           In our quest for solution methods, we start with finding solutions
           to certain first order differential equations.
           Example
           Solve the differential equation dy = x + 1 − sinx.
                                                               dx
                                        Z dy dx = Z (x +1−sinx) dx
                                             dx
                                                       x2
                                               y = 2 +x +cosx +C
           When can we solve a differential equation in this fashion?
    Solving Simple Differential Equations           Separable Variables            Revisiting IVPs and Models            Conclusion
    When Can we Solve with Integration Alone?
           Differential equations for which a solution can be found by simple
           integration are called separable.
           Separable DEs
           Afirst order DE of the form dy = f(x,y) is said to be separable,
                                                            dx
           or to have separable variables if we can rewrite f (x,y) as
           f (x,y) = g(x)h(y).
           Example
           Which of the differential equations below are separable?
                   dy =xsiny +3xey
                   dx
                   dy =ex +ey
                   dx