Separable Differential Equations 7.3 Separable Differential Equations M.L.King Jr. Birthplace, Atlanta, GA Greg Kelly Hanford High School Richland, Washington Photo by Vickie Kelly, 2002

Separable Differential Equations 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 y2 to separate the variables. (Assume y2 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 9: Separable differential equation Combined constants of integration

Example 9: 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.

In another generation or so, we might be able to use the calculator to find all integrals. Until then, remember that half the AP exam and half the nation’s college professors do not allow calculators. You must practice finding integrals by hand until you are good at it! p