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Math Help - Initial Value problem

  1. #1
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    Initial Value problem

    Hi, i have this initial value problem for y(0) = 1 and the following equation :

    dy/dt = ( y + 1/y ) * 1/2

    The question asks to prove the solution is:

    y = sqrt( 2*exp(x) - 1 )


    I am confused as to where the extra variable x comes from ?
    any help apprieciated, thnks in advance
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Richyie View Post
    Hi, i have this initial value problem for y(0) = 1 and the following equation :

    dy/dt = ( y + 1/y ) * 1/2

    The question asks to prove the solution is:

    y = sqrt( 2*exp(x) - 1 )


    I am confused as to where the extra variable x comes from ?
    any help apprieciated, thnks in advance
    Use:

    y = \sqrt{ 2\exp(t) - 1 }

    and you don't have to solve the IVP just show that this function satisfies both the DE and the initial condition.

    CB
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  3. #3
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    hi, thanks for the reply!

    im still abit confused to why in the question X is used instread of t, how are they interchangable ?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Richyie View Post
    hi, thanks for the reply!

    im still abit confused to why in the question X is used instread of t, how are they interchangable ?
    x and t are dummy variables it does not matter what they are called as long as you use the same name all of the time.

    The question has a typo it should have used t in the second equation.

    CB
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  5. #5
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    thanks ! , that was what was confusing me origionally
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