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Math Help - Drawing a DFQ solution using the equation.

  1. #1
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    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.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by aurora View Post
    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
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  3. #3
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    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.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by aurora View Post
    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
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  5. #5
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    Thanks.

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