Definition                    AnExample                    DoubleCheck
             Separable Differential Equations
                                      ¨
                           Bernd Schroder
        ¨                                                      logo1
  BerndSchroder                      Louisiana Tech University, College of Engineering and Science
  Separable Differential Equations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       1. A separable differential equation is of the form
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          y′ = f(x)g(y).
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       2. That is, a differential equation is separable if the terms that
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             ′
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          are not equal to y can be factored into a factor that only
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          depends on x and another factor that only depends on y.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       3. The solution method for separable differential equations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          looks like regular algebra with the added caveat that we use
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          integrals to undo the differentials dx and dy from y′ = dy.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    dx
  Definition                         AnExample                           DoubleCheck
  WhatareSeparable Differential Equations?
         ¨                                                                 logo1
  BerndSchroder                             Louisiana Tech University, College of Engineering and Science
  Separable Differential Equations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       2. That is, a differential equation is separable if the terms that
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             ′
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          are not equal to y can be factored into a factor that only
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          depends on x and another factor that only depends on y.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       3. The solution method for separable differential equations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          looks like regular algebra with the added caveat that we use
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          integrals to undo the differentials dx and dy from y′ = dy.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    dx
  Definition                         AnExample                           DoubleCheck
  WhatareSeparable Differential Equations?
         1. A separable differential equation is of the form
            y′ = f(x)g(y).
         ¨                                                                 logo1
  BerndSchroder                             Louisiana Tech University, College of Engineering and Science
  Separable Differential Equations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       3. The solution method for separable differential equations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          looks like regular algebra with the added caveat that we use
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          integrals to undo the differentials dx and dy from y′ = dy.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    dx
  Definition                         AnExample                           DoubleCheck
  WhatareSeparable Differential Equations?
         1. A separable differential equation is of the form
            y′ = f(x)g(y).
         2. That is, a differential equation is separable if the terms that
            are not equal to y′ can be factored into a factor that only
            depends on x and another factor that only depends on y.
         ¨                                                                 logo1
  BerndSchroder                             Louisiana Tech University, College of Engineering and Science
  Separable Differential Equations