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Math Help - graphical represtation of a diff equation solution

  1. #1
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    graphical represtation of a diff equation solution

    the theory says that even without having the solution of the diff equation
    for any given (x,y) we could know the slope of the solution at this point.

    if we draw a line threw every point with the solpe of the solution we get the photo
    if we find a line wich is tangent to the lines then its the solution
    if we found the solution then in each one of its points its tangent to the collection of the grath.

    for this equation
    y'=y/x
    the direction graph is given by the following photo.
    i dont know how they made this graph.
    i dont have the idea of how to find the slopes at point (x,y)

    we have y/x x cannot be 0 thats it

    that line collection is some collection of lines y=x y=2x y=-x etc...
    i dont know how it correspond to y/x
    Last edited by transgalactic; October 8th 2010 at 06:33 AM.
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  2. #2
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    Quote Originally Posted by transgalactic View Post
    the theory says that even without having the solution of the diff equation
    for any given (x,y) we could know the slope of the solution at this point.

    if we draw a line threw every point with the solpe of the solution we get the photo
    if we find a line wich is tangent to the lines then its the solution
    if we found the solution then in each one of its points its tangent to the collection of the grath.

    for this equation
    y'=y/x
    the direction graph is given by the following photo.
    i dont know how they made this graph.
    i dont have the idea of how to find the slopes at point (x,y)

    we have y/x x cannot be 0 thats it

    that line collection is some collection of lines y=x y=2x y=-x etc...
    i dont know how it correspond to y/x
    The slope of a curve at a point (x, y) is given by dy/dx. And the differential equation tells you the rule for dy/dx ....

    I srongly suggest you review your class notes or textbook (or use Google to find appropriate websites) on slope fields.
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