Ch 13: Differential Equations

About This Chapter

Watch informative differential equations video lessons. Learn about a wide range of differential equations topics, including differential notation, proportional population dynamics and more.

Differential Equations

Differential equations have derivatives of variables in the equations. You may recognize it when you see d/dx before a variable. In these equations there can be either ordinary or partial derivatives.

Discover how differential equations may be used in physics through notation. These can be found in many areas of science and math, including algebra. Then you can learn how to solve system differential equations. These can be solved by separating variables in equations in a divide-and-conquer method.

These engaging videos cover some of the unique problems that are often seen in math. You may have heard the two-trains-leave-a-station word problem many times. Watch these lessons to find out how to solve this type of problem, specifically by using the distance-between-moving-points equations. Also, learn how to solve population dynamics problems. Finally, learn how to handle everyday equations, such as the draining-tank and painting-surface-area problems.

Many of these problems can be found in common situations during your daily life. By studying these principles, you'll grasp a basic understanding of calculus, physics, algebra and other types of math and science, looking at the roles they play in real life.

5 Lessons in Chapter 13: Differential Equations
Test your knowledge with a 30-question chapter practice test
Differential Notation in Physics

1. Differential Notation in Physics

Stop. Look around. Everything is changing. In this lesson, you'll learn what a differential equation is and how these equations can describe the world around you.

Separation of Variables to Solve System Differential Equations

2. Separation of Variables to Solve System Differential Equations

In this lesson, we discuss how to solve some types of differential equations using the separation of variables technique. We'll ponder the dastardly deeds of a mad scientist, using his chemical concoction as an example for how to use separation of variables.

Calculating Rate and Exponential Growth: The Population Dynamics Problem

3. Calculating Rate and Exponential Growth: The Population Dynamics Problem

You know how the world population keeps increasing? It's increasing faster now than it was 100 or 1,000 years ago. In this lesson, learn how differential equations predict this type of exponential growth.

Related Rates: The Draining Tank Problem

4. Related Rates: The Draining Tank Problem

Grab an empty cup and pour some water into it. In this lesson we will watch how the height of the water changes as we learn about related rates of change and learn how to solve the draining tank problem.

Related Rates: The Distance Between Moving Points Problem

5. Related Rates: The Distance Between Moving Points Problem

Remember the classic problem of math horror stories everywhere? You know, where one train leaves Kentucky at 2 p.m. and another leaves Sacramento at 4 p. m.? In this lesson, tame the horror and learn how to solve these problems using differentiation and related rates.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.