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Homework Help
Calculus and Beyond Homework Help
Slope Fields and Determing Behavior of Any Solution
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[QUOTE="Bashyboy, post: 4516520, member: 333236"] [h2]Homework Statement [/h2] The differential equation is y' = y^2 Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t →∞. If this behavior depends on the initial value of y at t =0, describe this dependency.[h2]Homework Equations[/h2] [h2]The Attempt at a Solution[/h2] Okay, so I plotted the slope field by evaluating the derivative at several different y-values. This is what I observed: The solution curve certainly depends on the initial y-value when t=0. If particular solution y(t) to the DE has a solution of the form (t=0, y>0) (passes through a point), then as t----> infinity, y(t)----> infinity. On the other hand, if some particular solution y(t) passes through a point of the form (t=0, y<0), then as t--->infinity, y(t)----> 0 Are these correct observations; and have I used terminology and notation correctly? Also, when considering solutions that pass through the negative portion of the y-axis, will some approach y=0 more quickly than others? [/QUOTE]
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Slope Fields and Determing Behavior of Any Solution
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