Second order homogeneous linear differential equations with constant coefficients

This differential equation tutorial will cover the method of solving differential equations with constant coefficients. This is an example of auxiliary equations with distinct roots.

#differentialequation #math #blackpenredpen

[jellybabiesarecool]

Some people make this stuff seem so complicated but when you explain it it's so simple.

[tahukediri]

this is beautiful, my lecturers never explain the origin of the identity equation (ar²+br+c) and here i am fascinated

[jhn]

wow!
factoring the quadratic equation was really an amazing technique.

[suellenalmeida]

I'm a Brazilian Student.Thank you so much! Your explanation helped me a lot :D

[robinamar]

Thanks a ton for posting logically relevant videos which present the real flavor of mathematics instead of the dumb, dry & non-connected list of formulas which is taught in the high school to majority of the students!
Please keep on preparing new videos on other key topics of mathematics!
Thanks again :)

[jamesvarner]

Why is he carrying a Halo plasma grenade?

[yamunanagaraj]

thank you man...
this video really helped me

[Kicsa]

I have an exam this weekend, I think after watching your methods i'll be more confident in my work, thanks!

[juanvalencia]

your videos are insanely clear and easy to follow!

[irisce]

your videos are the best BPRP! I learned all of these techniques in math classes at universities where most of the course was focused on teaching these techniques and solving tons of practice problems through rote memorization, but now that I'm in my upper level engineering classes and starting to need to recall these techniques, I remember none of them because I never learned the underlying reasons behind the techniques! Watching your videos gave me understanding that I never had before, all packed in short form video content. Now I understand them and won't forget how to solve them. Super super valuable to me. Thank you!

[myzorro]

FORMIDABLE ce que fait ce garçon. Toujours limpide et d une clarté et intelligence sans pareille. Merci à ce GRAND MONSIEUR !!!!😊😊

[taekwondotime]

I wish he would put *all three cases* in the same video. Also, a lot of people may find that using the *quadratic formula* is much easier and less error prone than factoring, and it always works whereas factoring does not. The first time you run into one of these problems on an exam they'll probably stick you with something that doesn't factor OR you'll get a problem that has imaginary numbers in it, so this case is the most ideal case you can possibly get, but prepare yourself for something much nastier on an exam. :)

[FF-iesd]

for those who wondering why y has to be equal to e^rt, here's my approach: FIRST!! Since it's a linear equation, y cannot have any power higher than 1. You might think it what if y=some constant, but then y' will be equal to 0, and so is y''. So if y = constant, then the whole equation becomes : a*0+b*0+cy=0, then c =0. But the constants "abc" are always given, if c has to equal to 0, then the question will be like this: 0=0, which is lmfao. SECOND!!!, since it's a linear DE, then y cannot be inside of any function, for example, ln(y), sin(y), etc. Then it leaves only one thing that remains non-zero after million times of differentiation: e^rt, where r is a constant.

[cristinamendozar]

This was a really nice explained video, I appreciate the time you have taken to do it! Thank you :)

[lLl-flrv]

From Canada, I say thank you very much man!!! You saved my life

[mmka]

You are a very nice man and your teaching is really interesting! I appreciate your explanation! Thanks a lot!

[tommyrosendahl]

This is a really advanced episode of Dora the Explorer...

[JesusGarcia-oxjj]

I agree please do more differential equations questions.

[cesarvillegas]

By far the best video about this topic I have ever seen!!!

[noonesherem]

oh my god. dude you are a legend!!! i spent all day trying to figure this out because my textbook didn't explain it hahaha thank you