Watching this video makes me really question why I even bother going to my lectures, I just spent an hour sitting in a lecture, bored out my mind and I left understanding none of it. I spend 20mins watching this video in the comfort of my home and I now understand it perfectly.
Spent over an hour in office hours with my prof + sat through class this was "taught" in + recitation it was "reviewed" in and I didn't understand until today with your video, my exams tomorrow thanks!
All coefficients must be zero on the left side, to ensure the polynomial is zero for all x values. Similar to comparing coefficients in certain types of algebra solutions (comparing coefficients in partial fractions, for example).
It is not about two things adding to be zero. It is about comparing coefficients for the power series. For a power series to be guaranteed to be zero, then every coefficient must be zero. Consider: a + bx + cx^2 + dx^3 = 0 for instance. If a, b, c, or d are not zero, then the left side is not guaranteed to be zero (depending on what you put in for x).
Lol @ 14:35 - "no more math," I actually find the recursion and patterning in these to be really remarkable. I just have a hard time making the recursion relation up at the end out of it, especially since often there isn't one that is really easy to identify. Like this one, it is y_1(x)=a_0*sum_(n=0)^\infty x^{3n} and y_2(x)=a_1sum_{n=0}^\infty x^{3n+1}, but I can't easily see a pattern to the coefficients within the terms. Do you know of a good material for finding out how to do this more easily? Or is there just no point in doing that, and if that is the case why does my professor keep doing that?? LOL
Watching this video makes me really question why I even bother going to my lectures, I just spent an hour sitting in a lecture, bored out my mind and I left understanding none of it. I spend 20mins watching this video in the comfort of my home and I now understand it perfectly.
Explained better in 18 minutes than my prof in two lectures.
Well done.
2 weeks of confusion solved in 20 minutes. Thank you very much!
I can't believe I spent almost two weeks trying to solve this with no success!!! Thank you sir.
Very helpful...finally cleared up the indexing issues I was encountering after reading numerous textbooks. Pretty clear now. Keep it up!
God, my lecturer took entire week to explain this, still i couldn't understand the concept. You should be the professor in my university.
I arrived 7 years after you posted this video. Thank you.
Tomorrow is my exam and you just saved my semester
U r a blessing for all the students out here... :) Thanku for a clear explanation of the concept..!! Ur awesome..
Spent over an hour in office hours with my prof + sat through class this was "taught" in + recitation it was "reviewed" in and I didn't understand until today with your video, my exams tomorrow thanks!
Love, love, LOVE this video. Very clear and concise. Thank you so much!
wow :)
The Lecture was really outstanding.Things are very clear now.Thanks for your effort.
Do U know ?
U r a great man !!
My final is in few hours . This was really helpful and easy to understand u saved me . Thank you .
Great vid! That re-indexing process had me so confused I really think I can do this now
You are the greatest video on the internet!
Concepts got clear in the very first time (y)
OMG!!! Thanks to you I just aced my 4th diff eq test. you are truly a blessing. I finished with an overall grade of 91.3%
Finally,searched a lot for this topic...peace
How do you solve initial value problems?
You have explained very well this course, thanks for your contribution in science
life saviour mate :) ur saving my semester rn
A black background with the perfect voice.
That's it, that's enough!!!
thank you so much this was really well explained! And used a pretty good example (Y)
This just made all of this make sense! Thank you!
This was unbelievably helpful! Thank you so much!!
Thanks, your thoroughness really helped me!
i needed video like this.... and you are saver.........
I thank God for bringing you in this third planet
@8:14 why is 2A_2=0 a possibility if its addition not multiplication?
All coefficients must be zero on the left side, to ensure the polynomial is zero for all x values. Similar to comparing coefficients in certain types of algebra solutions (comparing coefficients in partial fractions, for example).
Thanks so much! You explained this so well!
thanks for your help . i have an exam and that's really help
Best👍🏻👍🏻
Explain very well ..😇
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That is really help me. Thank you very much. 💌
Very clear explaination thnk yu :-)
that was extremely helpful. Thanks!
Thank you for your efforts ❤️❤️👍
you sir you really saving my ass. Thank you very much!!!!!
Wow that is good
Easy to understand
very nice
you made it easy as butter
8:04 you lost me here. If a sum of 2 numbers is zero, why must either of them be zero? That’s only true when multiplying not adding.
It is not about two things adding to be zero. It is about comparing coefficients for the power series. For a power series to be guaranteed to be zero, then every coefficient must be zero.
Consider: a + bx + cx^2 + dx^3 = 0 for instance. If a, b, c, or d are not zero, then the left side is not guaranteed to be zero (depending on what you put in for x).
@@HoustonMathPrep Ok, thanks, I think I'm seeing this now.
Thanks for helping me understand this
Thanks...well explain.
Seriously good man
This is fantastic; thank you!
Great video thanks!
you are a god sir !!!
Lol @ 14:35 - "no more math," I actually find the recursion and patterning in these to be really remarkable. I just have a hard time making the recursion relation up at the end out of it, especially since often there isn't one that is really easy to identify. Like this one, it is y_1(x)=a_0*sum_(n=0)^\infty x^{3n} and y_2(x)=a_1sum_{n=0}^\infty x^{3n+1}, but I can't easily see a pattern to the coefficients within the terms. Do you know of a good material for finding out how to do this more easily? Or is there just no point in doing that, and if that is the case why does my professor keep doing that?? LOL
Many thanks for the video!
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Thanks alot 🌹🌷
nice
thanks man.....🙆🙆🙆🙆
Thank you 🌷
This is maaaaad long! Thanks though! :)
I feel like I just ran a marathon
THANK YOU
that was good
great video! but has anyone ever told you that you sound like Sheldon Cooper?
Houston math prep you are mathematician
Lifesaver
THANKS (with capital letters)
thank you
fanatstıcly solved
ı couldnt understand from books
omg cant be better ,
Thank you 🙏