1. Separable Differential Equations

2. A separable differential equation can be expressed as the product of a function of x and a function of y. Example: Multiply both sides by dx and divide both sides by y 2 to separate the variables. (Assume y 2 is never zero.)

3. Separable Differential Equations A separable differential equation can be expressed as the product of a function of x and a function of y. Example: Combined constants of integration

4. Example : Separable differential equation Combined constants of integration

5. Example continued: We now have y as an implicit function of x. We can find y as an explicit function of x by taking the tangent of both sides. Notice that we can not factor out the constant C, because the distributive property does not work with tangent.

6. Acknowledgement I wish to thank Greg Kelly from Hanford High School, Richland, USA for his hard work in creating this PowerPoint. http://online.math.uh.edu/ Greg has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum. www.mathxtc.com Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au 