All AP Calculus BC Resources
Example Question #1 : Modeling By Solving Separable Differential Equations
Solve the separable differential equation
with the condition .
To solve the separable differential equation, we must separate x and y, dx and dy respectively to opposite sides:
Integrating both sides, we get
The rules of integration used were
The constants of integration merged into one.
Now, we exponentiate both sides of the equation to solve for y, and use the properties of exponents to simplify:
To solve for C, we use our given condition:
Our final answer is