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Math Help - confirmation in regards to this question

  1. #1
    Junior Member
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    confirmation in regards to this question

    Hi all,

    I recently posted 'want some confirmation' and it was in relation this question:

    dy/dx = (5x^2)(cos^2(y)) for y(1) = 5*pi

    i get y = arctan[ 5/3 (x^3 -1)]

    however the answer states y = arctan[5/3 (x^3 -1)] + 5*pi...

    I have no idea where that 5*pi is coming from hence it lead to the post earlier.

    Thanks in advance,
    ArTiCk
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I recently posted 'want some confirmation' and it was in relation this question:

    dy/dx = (5x^2)(cos^2(y)) for y(1) = 5*pi

    i get y = arctan[ 5/3 (x^3 -1)]

    however the answer states y = arctan[5/3 (x^3 -1)] + 5*pi...

    I have no idea where that 5*pi is coming from hence it lead to the post earlier.

    Thanks in advance,
    ArTiCk
    Assume that:

    y(x) = \arctan[ (5/3) (x^3 -1)]

    is a solution to your ODE, then so is:

    y(x) = \arctan[ (5/3) (x^3 -1)]+k

    for some constant k.

    You have to choose k so that the condition y(1)=5 \pi is satisfied, and for that you need k=5 \pi.

    So the solution to your ODE and condition is:

     <br />
y(x) = \arctan[(5/3) (x^3 -1)] + 5 \pi<br />

    RonL
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  3. #3
    Junior Member
    Joined
    Mar 2008
    Posts
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    Hi all,

    could someone post full working out please because i still can't get the answer. When i do it, i get c = tan(5*pi) -5/3

    y = arctan( (5/3)x^3 + c)

    Thanks,
    ArTiCk
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