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i need to find the extremal of the functional $\int I(y,y'') dt$. Could anyone tell me the concepts of finding the extremal so that i can go about solving this one?

Update:

So my function was: G= $\int(ay+ $$\frac{1}{2}$$ b$y''^2$ )dt$ solving it using using the Euler–Lagrange equation as given in the link below, we get:

a+by''''=0

which on solving gives:

y=-(a(t^4))/(24b).

Am i right in solving this one?

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    have you tried http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation#Single_function_of_single_variable_with_higher_derivatives (Euler-Lagrange equations - the link is to the case of higher derivatives, since you need it)?2011-04-10
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    for some reason my link doesn't go where it's supposed to, so go to the "Single function of single variable with higher derivatives" case2011-04-10
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    look up "calculus of variations" and "euler lagrange equations". there's also a cheap, easy to read dover book by gelfand and fomin entitled "calculus of variations"2011-04-10
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    @user8286 thank you, the link was very helpful!!!2011-04-10

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