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Math Help - Help me with this Differential equation

  1. #1
    lo2
    lo2 is offline
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    Help me with this Differential equation

    Hi there, the forum looks great.

    Now I have got this Differential equtation:

    \frac{dy}{dx}=2xe^{x}

    The function which is the solutions goes through (0,2). My solution is:

    y=2e^{x}(x-1)+4

    That is not the problem. The problem is that now I have to find an asymptote to the curve and I really cannot find any...

    So please help!

    I have typed the math stuff in LaTeX code I hope that you understand it.
    Last edited by lo2; August 20th 2006 at 01:57 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by lo2
    Hi there, the forum looks great.

    Now I have got this Differential equtation:

    \frac{dy}{dx}=2xe^{x}

    The function which is the solutions goes through (0,2). My solution is:

    y=2e^{x}(x-1)+4

    That is not the problem. The problem is that now I have to find an asymptote to the curve and I really cannot find.
    y is finite whenever x is finite; so there are no vertical asymptotes.

    As x \to \infty,\ y \to \infty so there is no asymptote as x \to +\infty, that
    leaves the possibility of an asymptote where x \to -\infty, and indeed
    checking we find that y=4 is an asymptote as x \to -\infty.

    You will find sketching the curve a great help with problems like this.

    RonL
    Last edited by CaptainBlack; August 20th 2006 at 04:00 AM.
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  3. #3
    lo2
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    Thanks for the help!

    I was just to focused on a vertical asymptote to like consider the possibility of a horicontal one.
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