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Thread: Separable Differential Equation: (t^2 + 16)dx/dt = (x^2 + 36)

  1. #1

    Separable Differential Equation: (t^2 + 16)dx/dt = (x^2 + 36)

    I have a problem I just can't seem to get right.

    (t^2 + 16)dx/dt = (x^2 + 36)

    So I know you have to get all the x's to one side and the t's to the other so I got this:

    1/(x^2 + 36) dx = 1/(t^2 + 16) dt

    Differentiate each side and you get:

    1/6arctan(x) = 1/4arctan(t/4) + C

    Now the part where im confused is how to isolate for x = ...

    I got arctan(x/6) = 6(1/4arctan(t/4) + C) and don't know how to proceed from here.

    Any help?

  2. #2
    Elite Member
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    Jun 2007
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    Quote Originally Posted by reconrusty View Post
    I have a problem I just can't seem to get right.

    (t^2 + 16)dx/dt = (x^2 + 36)

    So I know you have to get all the x's to one side and the t's to the other so I got this:

    1/(x^2 + 36) dx = 1/(t^2 + 16) dt

    Differentiate each side and you get:

    1/6arctan(x) = 1/4arctan(t/4) + C

    Now the part where im confused is how to isolate for x = ...

    I got arctan(x/6) = 6(1/4arctan(t/4) + C) and don't know how to proceed from here.

    Any help?
    Think about the definition of arctan(x) = Θ
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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