If you plug in the slope field dy/dx = x^2/y^2 into this generator, http://www.math.rutgers.edu/~sontag/...OdeApplet.html

How do you interpret that graph? Is that straight line that runs through the origin part of the solution?

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- Mar 27th 2013, 07:15 AMgoku900Slope Field
If you plug in the slope field dy/dx = x^2/y^2 into this generator, http://www.math.rutgers.edu/~sontag/...OdeApplet.html

How do you interpret that graph? Is that straight line that runs through the origin part of the solution? - Mar 27th 2013, 08:56 AMTheEmptySetRe: Slope Field
One way to think about slope fields is to imagine them like currents on a river. If you drop a cork into the river at a certin point (the initial condition) where will the cork go? The path of the cork will always be parallel to the flow lines. On the graph I "dropped" the cork in three different place (in three colors) and sketched a rought graph of what a solution would look like. All solutions are attracted to the line y=x.

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How do you interpret that graph? Is that straight line that runs through the origin part of the solution?

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