What are differential equations?

This video answers the following questions: What are differential equations? What does it mean if a function is a solution of a differential equation? Why are differential equations important?

Note: In this video, I don't explain why the real root of x^5 - x - 1 = 0 cannot be expressed in terms of radicals. This is an example of the "unsolvability" of quintic equations. For more on this topic, see the Abel-Ruffini Theorem and Galois Theory.

Image sources:
All other images in this video drawn by Matthew Wright.

[levimungai]

The definition, " A differential equation occurs when it is necessary to relate A QUANTITY GIVEN BY A FUNCTION to its RATE OF CHANGE GIVEN BY THE DERIVATIVE OF THE FUNCTION." just clears everything for me. Its a small point but it has been missed surprisingly by even popular books. Probably because the authors assume it is obvious. Good video.

[VishalPatel-dqdt]

A Million times better than boring college lectures.

[HashemAljifri]

I remember when I took this in engineering dynamics vibrations! It was so complex

[JefrilAmboy]

thank you for the explanation. I just have a comment on the last part, on the example of the PDE. I think its the heat equation instead of wave equation.

[marilenaisoardi]

Amazing job! All your explanations are so clear and the way you visualize them! Can I ask you what do you use to make them?

[ntfbnglz]

I’m in the beginning of my college career about to take Calculus 1, I’ve been told DE is a complete nightmare, I just hope it’s not as bad as people say it is

[macgaming]

Thank you sir, basic concept is understood Sir

[mast]

I find that people do not know how to make Maths simple. For example you use the word derivative assuming that e we know what derivative means. 🤦🏾‍♂️🤦🏾‍♂️