HW2 Q3.19(4)

1. 

   Lohit Gudivada @ 7:02 pm on 22 Sep 2017

   Shouldn't this problem specify some boundary conditions as well in order for us to solve for the constants?

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2. 

   Fei Tao @ 12:25 am on 24 Sep 2017

   Hi Lohit,

   I tried to solve this problem with the Euler-Lagrange equation with multiple functions. Then the two differential equations I got from the E-L equation lead y(x) = z(x) =0. Therefore, We do not need boundary conditions to solve this problem. I hope this is helpful. Let me know if you get more questions.

    

   Best,

   Fei Tao

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3. 

   Imad Hanhan @ 10:44 am on 25 Sep 2017

   Fei,

   Can you explain more how you got y(x)=z(x)=0?

   When I use the E-L equations for multiple functions (bottom of page 103) I get the following system of equations:

   2z-4y-2y''=0    ,    2y+2z''=0

   Any help or hints would be appreciated.

   Thanks,

   Imad

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4. 

   Akanksha Parmar @ 12:09 pm on 25 Sep 2017

   Hi Imad,

   I got the same expression as yours.

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5. 

   Fei Tao @ 2:46 pm on 25 Sep 2017

   Hi,

   I made a mistake in my code. Sorry about the confusion. I got the same expression as yours. Yes. We need four BCs to solve for the exact function. I used Mathematica to get the general solution of the system of differential equations. Attached is the result.

   Best,

   Fei

   

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6. 

   Akanksha Parmar @ 4:47 pm on 25 Sep 2017

   Also, Fei, your expression for 3.10 should have y'^2 and not just y'. Can you please check and let me know? Otherwise, I will have to do it again.

   Thanks,

   Akanksha

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7. 

   Fei Tao @ 4:57 pm on 25 Sep 2017

   Hi Akanksha,

   The attached picture used Samel's expression. I tried to use Mathematica to do this problem. However, it does not working very well. The general solution of y(x) is not very good. Attached is the expression I got from Mathematica. 

   Instead, I solved it by hand. The link below can give you enough info on how to solve it. 

   https://math.stackexchange.com/questions/1834585/curve-enclosing-the-maximum-area

   Let me know if you have more quesitons.

   Best,

   Fei 

    

   

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8. 

   Kunal Samel @ 5:12 pm on 25 Sep 2017

   I just replied to the discussion on 3.10, i think i have the same answer.

   with regard to 3.19(4), what can we conclude about the highlighted terms?

    

   

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