AP CALCULUS · MODULE 04

Differential Equations
Modeling Change

Learn how to model real-world problems using differential equations — separable equations, slope fields, logistic growth, and Euler's method.

📘 BUders Learning System

This module covers separable differential equations, slope fields, the logistic model, and Euler's method. Topics with 🔷 are BC Calculus only.

Separable Differential Equations

$\frac{dy}{dx} = f(x)g(y)$ — separating variables and integrating both sides to find general and particular solutions.

AB & BC → start

Visualizing differential equations by drawing short line segments representing the slope at each point.

AB & BC → start

Exponential Growth & Decay

$\frac{dy}{dt} = ky$ — solutions $y = y_0 e^{kt}$, half-life, doubling time, and real-world applications.

AB & BC → start

Logistic Growth Model

$\frac{dP}{dt} = kP\left(1 - \frac{P}{M}\right)$ — population growth with carrying capacity $M$.

AB & BC → start

Euler's Method (BC)

$y_{n+1} = y_n + h \cdot f(x_n, y_n)$ — numerical approximation for differential equations.

🔷 BC only → start

Practice Problems

20 solved problems covering all differential equation topics.

practice → start

20-question interactive quiz with instant feedback.

assessment → start