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Thread: Help me with this Differential equation

  1. #1
    lo2
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    Help me with this Differential equation

    Hi there, the forum looks great.

    Now I have got this Differential equtation:

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

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

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

    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; Aug 20th 2006 at 12:57 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:

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

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

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

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

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

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

    RonL
    Last edited by CaptainBlack; Aug 20th 2006 at 03:00 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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