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Math Help - [SOLVED] Ordinary differentiation equations (ODE)

  1. #1
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    [SOLVED] Ordinary differentiation equations (ODE)

    hey there..
    i've got unsolved question here..

    Question:
    Solve the initial value problem.
    2yy’ = x / √x^2 – 16 ; y(5) = 2

    2yy’ = x / √x^2 – 16
    2y dy/dx = x / √x^2 – 16
    ∫2y dy = ∫ x / √x^2 – 16 dx
    y^2 = √x^2 – 16
    y = (√x^2 – 16)^1/2





    my answer was wrong. the answer is y = ((√x^2 – 16) + 1)^1/2
    how am i going to get the correct answer..?
    and.. what is the use of y(5) = 2?
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  2. #2
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    Quote Originally Posted by nameck View Post
    hey there..
    i've got unsolved question here..

    Question:
    Solve the initial value problem.
    2yy’ = x / √(x^2 – 16) ; y(5) = 2

    2yy’ = x / √(x^2 – 16)
    2y dy/dx = x / √(x^2 – 16)
    ∫2y dy = ∫ x / √(x^2 – 16) dx
    y^2 = √(x^2 – 16) + C

    now use the given initial value to find the constant of integration, C ...

    2^2 = √(5^2 – 16) + C
    ...
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