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Math Help - finding an extremal

  1. #1
    Member
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    finding an extremal

    If , show that the extremal is

    I've done:




    Then using Euler's equation we get:



    So

    and then I'm stuck from here, I can't see how to turn this is into trigonometric functions? I tried letting which didn't work...

    Can anyone please help me?

    Thanks in advance!
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  2. #2
    MHF Contributor

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    Solve the differential equation 1- y"= y which is the same as y"+ y= 1. That's a linear equation with constant coefficients. Its characteristic equation is r^2+ 1= 0 and I recommend trying y= A, a constant, for the "specific solution".

    This problem clearly expects you to be able to solve that differential equation.
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