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Math Help - Differential equations with one variable

  1. #1
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    Differential equations with one variable

    Hi!
    I have some problems with solving the following differential equation:
    x' - x^{2} = 1
    where the unknown is x(t)
    It is probably not that difficult but I am unable to find any examples involving only one unknown.
    Any help would be appreciated!
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Uh...

    x' = 1 + x^2

    \dfrac{dx}{dt} = 1 + x^2

    \displaystyle \int \dfrac{1}{1+x^2}\ dx = \int\ dt

    ?
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  3. #3
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    Quote Originally Posted by masterk View Post
    Hi!
    I have some problems with solving the following differential equation:
    x' - x^{2} = 1
    where the unknown is x(t)
    It is probably not that difficult but I am unable to find any examples involving only one unknown.
    Any help would be appreciated!
    I would be very surprised at that! In every differential equations text book I have ever seen, MOST of the problems in at least the first several chapters have only one unknown!
    If, for example, you had an equation that said
    \frac{dx}{dt}- x^2= 1
    that is an equation that has "only one unknown"- x. The 'independent variable', t, is not an unknown. And, in fact, since you say that "the unknown is x(t)", the equation
    x'- x^2= 1
    is exactly the same as the equation
    \frac{dx}{dt}- x^2= 1.

    As Unknown008 said, that is a separable equation. Separate the variables and integrate.
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