6.4 day 1 Separable Differential Equations Jefferson Memorial, Washington DC Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2007

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.)

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

Example: Separable differential equation Combined constants of integration

Example: 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.

Use 2ND, = to get the prime symbol. To do the same problem on the TI-89: Enter the differential equation as shown: Use the multiplication symbol. Independent variable Dependent variable enter Press F3 Calc, C deSolve( to open the differential equation solver.

(Use copy and paste to insert the expression) To do the same problem on the TI-89: In this case, the calculator does not explicitly solve for y, so we can try using the “solve” function. This solution includes restrictions on the domain.  Highlight the solution and scroll right to see the rest of the answer. Press F3 Calc, C deSolve( to open the differential equation solver.