# Help me with this Differential equation

• Aug 20th 2006, 12:16 AM
lo2
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...

I have typed the math stuff in LaTeX code I hope that you understand it.
• Aug 20th 2006, 02:45 AM
CaptainBlack
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
• Aug 20th 2006, 02:48 AM
lo2
Thanks for the help!

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