Second Order Nonhomogeneous Cauchy-Euler Differential Equations

This video provides an example of how to find the general solution to a second order nonhomogeneous Cauchy-Euler differential equation.
Site: mathispower4u.com

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[@Mathispower4u]

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[@Mathispower4u]

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[@Mathispower4u]

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This one really helped me because my text had problems just like this but did not provide any examples.

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[@andrewchoi2780]

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.

[@laurentaylorhamilton]

this video really help me!!! as did the cute quote at the end. thanks for the reminder.

[@VikramSingh7]

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 :)

[@mikeahmed7092]

excellent explanation. Took my professor 3 days to explain it.

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I learned in 1 hour which my friends learned in 20 days....u are so osm

[@onurcagan7367]

Appreciate your help, one of the main guides I used to pass Differential Equations class. Thanks.

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A very clear and concise explanation! Thanks. Keep up the good work.

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helping out student who could fail...

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i love your videos! Clear explanation, i learn more with you than in class ahah !! Thank you

[@AjayKumar-vk4lj]

sir I think you have taken g(x) wrong while doing the variation of parameters..

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[@sinetembasikelelamsizazwe8943]

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.

[@JustSatoomi]

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[@shaftlereitie7403]

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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[@ankitjeezy]

This indeed was very helpful. Thanks for making this video.

[@mmmflyerr]

Very helpful... Thnx!! And great quote at the end

[@androidinf044]

your video helps a lot thanks sir.

[@sarahchacon3284]

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.

[@cloiu3311]

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?

[@emilygonzalez1024]

This video is incredible, thank you so much!

[@hectorojeda819]

Great video thanks.. eventhough English is my second language (y)

[@shubhamrawat1393]

Pls make a video of euler cauchy having same roots

[@djeroid2000]

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).

[@masong95]

djeroid2000 I believe you are able to multiply an "x" through the whole equation.

[@cestlavieeee]

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...

[@GoldenGloves1947]

These videos are excellent!

[@ethant4988]

can i use a different method here? like guessing a particular solution so that y_p = Ax ?

[@awt9805]

anyone has a link to solve a cauchy-euler equation using the substitution x=e^t instead?

[@jacobdiaz2935]

Can someone explain how he got the y1 and the y2?

[@Tofumoode-jy6ro]

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.

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[@aladdinkayqubad1645]

Thank you Sir!!!!!!!!!

[@shirosensei3565]

if g(x)=cosx can i use that way?

[@lazypunk794]

My teacher taught us a method to solve this problem by taking x=e^t. i was hoping to see that.

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How did you determine y1 and y

[@kajalojha3181]

what if power of x is lower than y in question?

[@ThePoshboy1]

I'm literally in the middle of an exam watching this :)

[@pelajaree]

Thank you so much

[@syahmim4867]

what about the root (m=0)? that's mean no homogenous solution right? reply fast

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Thank you!! Legend!

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[@froopi2]

Thanks!

[@Bedocalaway]

What if the first term wasn't x^2 & the second order & the prof asked for using Cauchy? :/

[@alexisbrazier1167]

At 4:55, how do we know that y1=x^2 and y2=x ?

[@masong95]

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.

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its very easy to get understand by an average student too

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