Help me with this Differential equation

**lo2** · August 20th 2006, 12:16 AM

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.

**CaptainBlack** · August 20th 2006, 02:45 AM

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

**lo2** · August 20th 2006, 02:48 AM

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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