Hello!

I was wondering. Say I'm given th diffrential euqation y' = f(x,y). Is there any way I can draw, at least approximately, the graph of the solution y(x), without solving the equation?

Thanks!

Tomer.

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- May 21st 2008, 10:42 AMauroraDrawing a DFQ solution using the equation.
Hello!

I was wondering. Say I'm given th diffrential euqation y' = f(x,y). Is there any way I can draw, at least approximately, the graph of the solution y(x), without solving the equation?

Thanks!

Tomer. - May 21st 2008, 11:08 AMtopsquark
Slope fields is what you want.

-Dan - May 21st 2008, 11:18 AMaurora
Thanks for the response.

I figured as much, but I'm having a hard time drawing a slope field for

y'=x^2 * siny.

That's a strange thing. This excercise is under the title " the Uniqueness and Existence sentence", but what they ask me to do is to sketch the solutions (notice the 's' in solutions) of the problem. As far as I understand, this problem has only one solution, given a side condition (y(x0)=y0), and it is defined on all of R.

Should I just draw the solution's graph or what?

:-\

Thanks. - May 21st 2008, 11:23 AMtopsquark
- May 21st 2008, 11:36 AMaurora
Thanks.

Can you confirm, however, that this equation has indeed only one solution, given a side condition?