# is my solution correct?

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• Feb 5th 2010, 09:56 PM
lollol
is my solution correct?
Hi, i attempted this question, but not sure whether it is correct or not..(Happy)

using separation of variables:

X''(x)=S X(x) , Y''(y)=-S Y(y), where S is separation constant

becos X'(0)=0, X'(1)=0, so using the boundary value table i get:

S=(npi)^2

X=cos(n pi x) n=0,1,2....

Y=Acos*square root of S * y + Bsin* square root of S * y

since Y(0)=0

so Y=Bsin(n pi y)

so X(x)Y(y)=Bcos(n pi x)* sin(n pi y)

i know it's not finished, but is it correct from here? cos i dont feel quite sure about it....thank you~(Hi)
• Feb 6th 2010, 06:29 AM
HallsofIvy
Quote:

Originally Posted by lollol
Hi, i attempted this question, but not sure whether it is correct or not..(Happy)

using separation of variables:

X''(x)=S X(x) , Y''(y)=-S Y(y), where S is separation constant

becos X'(0)=0, X'(1)=0, so using the boundary value table i get:

S=(npi)^2

No, that's impossible. If X is a trig function (and it must be for its derivative to be 0 at 0 and 1), then S must be negative: you must mean $S= -(n\pi)^2$.

Quote:

X=cos(n pi x) n=0,1,2....

Y=Acos*square root of S * y + Bsin* square root of S * y
and now, because S is negative, -S is positive. $Y"= n\pi Y$ so Y is exponential or hyperbolic: I would use Y(y)= C cosh(y)+ D sinh(y) because then Y(0)= C cosh(0)+ D sinh(0)+ C(1)+ D(0)= C= 0.

Quote:

since Y(0)=0

so Y=Bsin(n pi y)

so X(x)Y(y)=Bcos(n pi x)* sin(n pi y)

i know it's not finished, but is it correct from here? cos i dont feel quite sure about it....thank you~(Hi)
• Feb 6th 2010, 04:40 PM
lollol
thanks hallsofivy, from ur solution, i would get Y=Dsinh(n pi y), and for X, since

http://www.mathhelpforum.com/math-he...bc47fa0b-1.gif. so it involves complex number after substituting S into the equation,
therefore X=Acos(n pi x) + Bsin(n pi x)

does it seem right?(Lipssealed)
• Feb 7th 2010, 03:24 AM
HallsofIvy
Yes, you had X correct all along: X(x)= A cos(n pi x).

Your entire solution will be a sum such as $\sum_n C cos(n\pi x)Sinh(\pi y)$.
• Feb 10th 2010, 02:23 AM
lollol
hi
sry.. but i think i am stuck again..while i continue with my work, i got An=0..(Headbang) i dont quite understand why i got that, so i think may be i am wrong?(Worried) please see the attachment, thank you