That is a bit different. If the Cauchy-Euler equation is order 3, then your equation for m is a bit different. Rather than having to remember a different "equation for m" for each order, I might recommend the following: 1) First, solve the homogeneous version of the equation by plugging in x^m for y and solving the "equation for m" that you get from that. 2) Once you have the function that is a solution for the homogeneous equation, you could use variation of parameters to solve the remaining particular function, since your right hand side is ln(x). Our video on solving 2nd-order non-homogeneous Euler equations can be found here: ruclips.net/video/KTx6KXcJwSA/видео.html You would simply adapt this to your 3rd-order problem. Good luck!
Just wow. I don't even to go lectures because my professor cannot teach and I cannot understand his accent. I find every topic for my differential equation class on this channel. May god bless you and your family. Thank you sir!
Thank you so much for the efficient explanation...my university professor took a whole 55 minute lecture just to teach Cauchy-Euler Differential Equations. PS your handwriting is so pleasing to look at
Thanks, Alex! I don't figure that most people will watch a 55 minute RUclips on something, so that is avoided on this platform. 🤣 If I were presenting this to an actual in-person class, I might go into just a few more details than seen here. Either way, thanks for your kind words. We are happy to have helped you!
Hey houston, I am back again. Your constant student and subscriber. You are an amazing teacher and my all time DEs saviour. Thanks a lot. :)
Welcome back!
@@HoustonMathPrep hey houston, a doubt! What if the cauchy-euler equation has an order 3 and has F(x)=ln(x)?? I am unable to figure out.
That is a bit different. If the Cauchy-Euler equation is order 3, then your equation for m is a bit different. Rather than having to remember a different "equation for m" for each order, I might recommend the following:
1) First, solve the homogeneous version of the equation by plugging in x^m for y and solving the "equation for m" that you get from that.
2) Once you have the function that is a solution for the homogeneous equation, you could use variation of parameters to solve the remaining particular function, since your right hand side is ln(x). Our video on solving 2nd-order non-homogeneous Euler equations can be found here: ruclips.net/video/KTx6KXcJwSA/видео.html
You would simply adapt this to your 3rd-order problem. Good luck!
This is wonderful! 😊 You videos help me fill in the gaps in my math background! Much appreciated! ❤
By far the best video I've seen that explains Cauchy-Euler Differential Equations. Thank you!
Wow, thank you for that!
Thank you sooooo much for this! I really needed this level of intuitiom=n :)
Glad it was helpful!
Just wow. I don't even to go lectures because my professor cannot teach and I cannot understand his accent. I find every topic for my differential equation class on this channel. May god bless you and your family. Thank you sir!
I'm glad that these are helping you! Best of luck in your class!
You're an incredibly effective and efficient lecturer. Thank you very much!!
Thanks for taking the time to share the nice thoughts! It is appreciated.
Best channel for differential equation!!
Very clear and concise with helpful examples, definitely would recommend as supplementary self-study.
Thank you for sharing your positive impression!
Just in time for my course! Thank you again! Will you be releasing a linear algebra course?
We certainly will! Unfortunately, we have other courses we are building soon, so linear algebra will not be built until 2022.
thank you i realy understand cauchy euler bc of this vid!
I'm so glad!
Thank you so much for the efficient explanation...my university professor took a whole 55 minute lecture just to teach Cauchy-Euler Differential Equations.
PS your handwriting is so pleasing to look at
Thanks, Alex! I don't figure that most people will watch a 55 minute RUclips on something, so that is avoided on this platform. 🤣
If I were presenting this to an actual in-person class, I might go into just a few more details than seen here. Either way, thanks for your kind words.
We are happy to have helped you!