A differential equation is a type of equation in which at least one of the variables is a derivative. Due to the nature of differential equations and the integrals used in solving them, only a fraction of differential equations are solvable, and only a fraction of those are solvable by the methods available in the scope of the AP Calculus BC course. One very common application of the differential equation is for modeling exponential growth and decay.

As previously mentioned, not all differential equations are solvable. The only available method for solving differential equations within the scope of our course is by isolating variables. That is, treat the derivative as the fraction dy/dx, and isolate all x terms with dx and all y terms with dy and integrating. Then simplify the equation and solve for constant values given any variable values that you are given.

## Differential Equations

A differential equation is a type of equation in which at least one of the variables is a derivative. Due to the nature of differential equations and the integrals used in solving them, only a fraction of differential equations are solvable, and only a fraction of those are solvable by the methods available in the scope of the AP Calculus BC course. One very common application of the differential equation is for modeling exponential growth and decay.

## Table of Contents

## Algebraic Approach

As previously mentioned, not all differential equations are solvable. The only available method for solving differential equations within the scope of our course is by isolating variables. That is, treat the derivative as the fraction

dy/dx, and isolate all x terms withdx and all y terms withdy and integrating. Then simplify the equation and solve for constant values given any variable values that you are given.## Example