# Drawing a DFQ solution using the equation.

• May 21st 2008, 11:42 AM
aurora
Drawing 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, 12:08 PM
topsquark
Quote:

Originally Posted by aurora
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.

Slope fields is what you want.

-Dan
• May 21st 2008, 12:18 PM
aurora
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, 12:23 PM
topsquark
Quote:

Originally Posted by aurora
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.

I'd sketch a few on scrap paper and give an answer that is "representative" of what the family looks like.

-Dan
• May 21st 2008, 12:36 PM
aurora
Thanks.

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