This video provides an example of how to find the general solution to a second order nonhomogeneous Cauchy-Euler differential equation. Site: mathispower4u.com
I hated the way this concept was presented in my textbook, by my professor and numerous websites. Thank you for your presentation. Elaborate, concise and to the point. Love it.
My professor skips this section idk why... but man this method is amazing. I was able to learn more from this 10 min video than from my PhD Math professor. I wish you were a professor at my University. #LEGEND
Thanks so much! This video is amazing and perfectly shows how this is solved. I can't believe I wasted so much time shuffling through stackexchange and trying to read lessons on solving non-homogeneous Cauchy-Euler ODEs when there's a video that helped me solve it in ten minutes.
I'm so lucky you uploaded this in the same semester I'm taking differential equations! Really nice work. These video are super helpful, can't thank you enough :)
What would be my y1 and y2 in case my roots are +/- 2i and my yc = c1cos(2lnx) + c2sin(2lnx)? Can you do an example on this type of problem but when you get complex roots? Thank you very much though it is very helpful! :)
Great Video. Question: why do we need to write (x^2y'')/x^2+(xy'/x^2)+(2/x^2)? [instead of just leaving the original equation]. Thanks for your help. Once again, great video.
What do you do in a situation where you have to use cauchy-euler, but the degree of the monomial coefficients are not equal to the order of the differentiation? (eg: xy"-3y'=0) There are a few like this in my Differential Equations book and the answers for the book I have dont explain how they even got to the auxiliary equation step in this kind of situation).
when we see an equation of that form, how do we know to perform variation of parameters method vs cauchy? They both look the same but when I try either method it gives different m values...
So, when I do complete the square. How do I know which one is y1 and y2?because I got (m-1) (m-2) In video, you got (m-2) (m-1) and y1 and y2 would totally be vice versa and the answer would totally be different.
Alexis Brazier the form is based off of your roots. For example, the roots were 2 and 1. Thus, you get c1x^(root 1)+c2x^(root 2). Replace root 1 and root 2 for whatever values you get for your roots.
You are my new best friend...I learned more in a 10 minute video than in a 2 hour lecture.
I'm glad I was able to help.
You're prolly the only reason I'll pass my ODEs exam tomorrow. You are a living LEGEND mate.
did you pass ?
@@Fundamental117 YES. Killed it. Got a B+.
@@tabsheerali6144 lmao hope I pull the same trick next week
I think I share the same sentiment with everyone else when I say that your contribution is invaluable to all of us. Thank you so much for doing this.
I wish I could like this video 10 thousand times. Thank you so much.
Thank you. I'm glad I could help.
Thanks, I'm glad you find them helpful. Please share them with others.
your channel should be called "mathmadeeasy4u" you do an excellent job explaining these things
I'm glad you have found the videos helpful!
Thank you! I wish I had more time to make more. I'll keep adding more, but am working on several topics at once. Glad to help.
I hated the way this concept was presented in my textbook, by my professor and numerous websites. Thank you for your presentation. Elaborate, concise and to the point. Love it.
Ngl, so far it took me almost 3 years to learn everything from high school and university. Absolutely love it, sir.
I have my ODE exam next week. If i pass, its all cos of you.
My professor skips this section idk why... but man this method is amazing. I was able to learn more from this 10 min video than from my PhD Math professor. I wish you were a professor at my University. #LEGEND
You are a sport! Thanks so much. May God keep inspiring you to help others and keep you in good health.
Thank you!
This one really helped me because my text had problems just like this but did not provide any examples.
THANKYOU!!! UGH. You literally helped me with two topics that i have been running away from since a week. GOD BLESS!
Thanks so much! This video is amazing and perfectly shows how this is solved. I can't believe I wasted so much time shuffling through stackexchange and trying to read lessons on solving non-homogeneous Cauchy-Euler ODEs when there's a video that helped me solve it in ten minutes.
this video really help me!!! as did the cute quote at the end. thanks for the reminder.
I'm so lucky you uploaded this in the same semester I'm taking differential equations! Really nice work. These video are super helpful, can't thank you enough :)
excellent explanation. Took my professor 3 days to explain it.
I learned in 1 hour which my friends learned in 20 days....u are so osm
Appreciate your help, one of the main guides I used to pass Differential Equations class. Thanks.
A very clear and concise explanation! Thanks. Keep up the good work.
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helping out student who could fail...
i love your videos! Clear explanation, i learn more with you than in class ahah !! Thank you
sir I think you have taken g(x) wrong while doing the variation of parameters..
All hail knowledge and people who are willing to share it.
Your videos are so helpful
Thanks for helping out man. You are a life saver.
I LOVE U omg this was sooo clear and simple
To find Yp, is it a math law to multiply the integrals by Y1 and Y2 respectively? The textbook I have been using does not multiply by them.
it would be great if you provide the presentation you are writing on
thank you
So enjoyable !!!!
Thanks 👍 👍👍
What would be my y1 and y2 in case my roots are +/- 2i and my yc = c1cos(2lnx) + c2sin(2lnx)? Can you do an example on this type of problem but when you get complex roots? Thank you very much though it is very helpful! :)
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This indeed was very helpful. Thanks for making this video.
Very helpful... Thnx!! And great quote at the end
your video helps a lot thanks sir.
Great Video. Question: why do we need to write (x^2y'')/x^2+(xy'/x^2)+(2/x^2)? [instead of just leaving the original equation].
Thanks for your help. Once again, great video.
On the slide shown at 4:36, why has the complimentary function form changed to have the second term as e as opposed to x?
This video is incredible, thank you so much!
Great video thanks.. eventhough English is my second language (y)
Pls make a video of euler cauchy having same roots
What do you do in a situation where you have to use cauchy-euler, but the degree of the monomial coefficients are not equal to the order of the differentiation? (eg: xy"-3y'=0) There are a few like this in my Differential Equations book and the answers for the book I have dont explain how they even got to the auxiliary equation step in this kind of situation).
djeroid2000 I believe you are able to multiply an "x" through the whole equation.
when we see an equation of that form, how do we know to perform variation of parameters method vs cauchy? They both look the same but when I try either method it gives different m values...
These videos are excellent!
can i use a different method here? like guessing a particular solution so that y_p = Ax ?
anyone has a link to solve a cauchy-euler equation using the substitution x=e^t instead?
Can someone explain how he got the y1 and the y2?
So, when I do complete the square. How do I know which one is y1 and y2?because I got (m-1) (m-2) In video, you got (m-2) (m-1) and y1 and y2 would totally be vice versa and the answer would totally be different.
+Ha Nguyen ......it doesnt matter as u will use the formula of wronksian in that it will sort them out .... do it once u will come know
Thank you Sir!!!!!!!!!
if g(x)=cosx can i use that way?
My teacher taught us a method to solve this problem by taking x=e^t. i was hoping to see that.
you are the real hero man
How did you determine y1 and y
what if power of x is lower than y in question?
I'm literally in the middle of an exam watching this :)
Thank you so much
what about the root (m=0)? that's mean no homogenous solution right? reply fast
Thank you!! Legend!
greet keep it up !!!!
Thanks!
What if the first term wasn't x^2 & the second order & the prof asked for using Cauchy? :/
At 4:55, how do we know that y1=x^2 and y2=x ?
Alexis Brazier the form is based off of your roots. For example, the roots were 2 and 1. Thus, you get c1x^(root 1)+c2x^(root 2). Replace root 1 and root 2 for whatever values you get for your roots.
its very easy to get understand by an average student too
Thank you so freaking much
thanks
Nice ... Very nice ...
Really Helpful.
thank you..:)
And the quotes >>>
yeah dat,s really helpful ^-^ . thanks bro..
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