HW2 Prob 3.10

1. 

   Kunal Samel @ 10:22 pm on 21 Sep 2017

   Hello everyone! I arrived at the following expression at the end of Problem 3.10

   (attached)

   any tips on integrating this would be greatly appreciated. Also, please comment if you got a different expression

    

   thanks

   Kunal

   

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2. 

   Fei Tao @ 10:31 pm on 21 Sep 2017

   I used Mathematica. Attached is the result from Mathematcia. 

   

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3. 

   Haodong Du @ 10:53 pm on 21 Sep 2017 — Edited @ @ 10:55 pm on 21 Sep 2017

   If you want to do this by hand, I can tell you my idea. Just replace y' with t. Then you would be able to separate t and x by lhs and rhs. Next step is just integration of something like dt/(1+t)^1.5. This could be solved by further replacing t with some sort of hyperbolic sine or cosine functions. Sorry that I don't have pen by hand, but I think it could be solved this way.

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4. 

   Kunal Samel @ 11:25 pm on 21 Sep 2017

   thanks a lot!...at least I arrived at the correct expression. I did try y' = t earlier and then t=tan(theta) but ended up with sininv(tan(something)) and stopped.

   I will proceed in mathematica

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5. 

   Kunal Samel @ 11:44 pm on 21 Sep 2017 — Edited @ @ 4:57 pm on 25 Sep 2017

   September 25 update: Mathematica is working now!.

   also i made an error in the denominator. It should be (1+(y'^2))^3/2 and numerator has a minus sign

   mathematica now gives a complex function as the answer...can anyone confirm?

   

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6. 

   Akanksha Parmar @ 5:10 pm on 25 Sep 2017

   Yes, but the expression in DSolve did not have y'^2 in the earlier picture you shared.

   Also, shouldn't the curve maximizing the area should be a circle(or a semi-circle)?

   Thanks Fei for the link, I will check it out.

   Thanks Kunal for clarifying the expression to me.

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7. 

   Akanksha Parmar @ 5:21 pm on 25 Sep 2017

   I used wolframalpha to solve this equation. It gave a good believable answer. Have a look, let me know if I made a mistake somewhere.

   

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8. 

   Fei Tao @ 5:21 pm on 25 Sep 2017

   Hi,

   Just realize the expression of y(x) I got from Mathematica is a function of circle. So Mathematica also works! :)

   

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9. 

   Akanksha Parmar @ 5:40 pm on 25 Sep 2017

   Yes, that is correct! Good point!

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10. 

    Lohit Gudivada @ 2:17 pm on 26 Sep 2017

    After solving the 2nd order ODE, we obtain the equation of a circle having 3 constants (c1, c2, lambda). After substituting the boundary conditions(y(x0)=y(x1)=0), I have been able to eliminate c2 and lambda. But c1 is still remaining.

    I know the 3rd equation that we should be using to eliminate c1 is the length equation (from where we can write c1 in terms of L). But I am unable to integrate the equation and solve c1 in terms of L. I have tried using mathematica also (which is not able to integrate the equation).

    Any help would be appreciated.

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11. 

    Lohit Gudivada @ 2:23 pm on 26 Sep 2017

    Here is a snippet of the mathematica file

    

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