Differential Equations: Lecture 2.3 Linear Equations

The book used for this course is Zill's Differential Equations. Here is my review of the book

[sueton]

This is how a person should teach something. Some fun here, some serious stuff there. Thanks for making this lecture public!

[emrongardizi]

0 dislikes for a reason. don't know how I would pass my DE class without this channel

[centralprocessingunit]

Your lectures are so good. I'm in high school and I had no knowledge or clue about what you did in these videos, but after watching on 2 of your lectures I can actually follow along!!!! so strong

[shaniceshipp]

Thanks for helping me learn Differential Equations during the pandemic.

[aldominicgatlabayan]

I've been watching his videos for sometime now since I started college, and I know many of his students already LOL. Hi Rafael and Anna. thank you sir, you made online learning a lot easier for me from the Philippines

[baron]

I am a junior in college taking this class and your lectures are very clear and easy to follow. Thank you for all the help.

[redandgreenchristmasblues]

you are an exceptional teacher! its so pleasant to hear laughter and see a smile during a lecture. you breaking it down into steps and demonstrating is very helpful!! :D

[lybakamran]

Thank you so much for saving my life by explaining in such a nice way! May god bless you Sirr!!

[JohnFL]

Thank You, Math Sorcerer! I was confused with the mu(x) term, but with your enjoyable explanation and the option to pause the lecture (which I can't do in class), I think I understand it better now. Also, I like how you threw in some made-up trivia about the letter mu, being based off the English alphabet instead of the other way around 🙃🐴

[mathiasjeppesen]

I am from Denmark, and I am in 10th grade! These lectures are really interesting and I am enjoying watching them!

[saidalmaqbali]

at the beginning of this semester I was so confused, but now I found my Salvador

[ashleyosorio]

I love your channel. It has been helping me out a lot. Thank you so much!!

[iremiposiajayi]

The question I have is why. Why does mu(x) work? Is there a proof to explain why choosing mu x this way and why following the steps ultimately leads to the product rule?

[sinuouslocks]

You are a gift from God! Muchisimas gracias, no sabe cuanto le agradezco que est`e subiendo estos videos.

[meetavdoshi]

for the very last problem, when you were doing the integration, would taking out 1/sec x be easier than the way you did it (avoiding the simple division of trig functions)? This would result in y=1/sec(x)*(tanx+c), then y=sinx(tanx+c), giving the answer of sinx + c(cosx). I guess it is one more step but the solution remains the same.

[koenth]

9:30 For me feels much easier just to realise that a negative power is 1 over a positive power, so
e^-ln|x| = 1/e^ln|x| = 1/|x|

[robn]

I understand the process and I understand what I call the reverse product rule step. Small question when computing the u(x) = e^(intergral(-1/x dx)) the answer given is e^(ln(1/x)). WHERE did the constant go like should the answer not be e^(ln(1/x)+c) => e^(ln(1/x)*e^(constant) ???

At about minute 18, Why don't we use the multiplication rule for y and x. I think that y is dependent on X.
I'd say (1/x)dy/dx - y/(x^2) = sin(x)

[sharifahmed]

Thanks prof: Sorcerer, you often mention a homework in your lecture in DE playlist, could you please kindly tell me where I can find it?. Thanks for your prompt response.

[iremiposiajayi]

First question: in the first example, can’t we just put the x’s on one side and the y’s on the other side like in separable DEs? How do you know when to use this method over separable?