function symmetric around a pointI need some quick help solving this:What is y(ln(2))if the function y satisfies d y d x = 1 − y 2 and is symmetric about the point (ln(4),0)?I know that a function is symmetric about the point (ln(4),0) if the function f defined by f ( x ) = y ( x + l n ( 4 ) )is odd, meaning f ( − x ) = − f ( x ) ∀ x )From formulas in my textbook, but I don't understand how to apply it correctly.

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function symmetric around a pointI need some quick help solving this:What is y(ln(2))if the function y satisfies            d      y              d      x        =  1  −      y    2  and is symmetric about the point (ln(4),0)?I know that a function is symmetric about the point (ln(4),0) if the function f defined by  f  (  x  )  =  y  (  x  +  l  n  (  4  )  )is odd, meaning  f  (  −  x  )  =  −  f  (  x  )  ∀  x  )From formulas in my textbook, but I don&#039;t understand how to apply it correctly.

enfujahl · Accepted Answer

The general solution to the differential equation is  y  (  x  )  =  tanh  ⁡  (  x  −      x    0    )where       x    0    is a constant to be determined. Since   tanh is symmetric (odd) around 0, you should choose       x    0    =  ln  ⁡  4 It is then easy to see that  y  (  ln  ⁡  2  )  =  tanh  ⁡  (  ln  ⁡  2  −  ln  ⁡  4  )  =  tanh  ⁡      (    ln    ⁡          1      2        )    =  −      3    5    .

function symmetric around a point I need some quick help solving this: What is y(ln(2))if the fun

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