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chapter2.page21 - • Do solutions display any periodicity...

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5. PHASE AND VECTOR FIELD DIAGRAMS 21 font. You can do this for headings etc. Graph Vector field Goal: Familiar your self with an many different kind of vector fields, defined by x 0 = f ( t, x ) , as possible and identify many general features of solutions, especially the following features, Does the equation has constant solutions? A constant solu- tion is shown in vector field as horizontal line segments since constant solution has slope equals zero. Does solutions converge to an particular solution in the lang run? Do solutions grow to infinite an a finite time? Her vertical bars indicate a solution might become unbounded in short time.
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Unformatted text preview: • Do solutions display any periodicity? We know sin( t ) has pe-riod of 2 π and solution curve repeats itself. Here large interval for t might be needed. You can use the following functions • f ( t,x ) = sin ( x ) • f ( t,x ) = cos ( t ) • f ( t,x ) = x ( x-1) • f ( t,x ) = e t x + sin ( x ) • f ( t,x ) = x + xsin ( t ) You should use the provide Mathcad file at the website www.unf.edu/ ∼ mzhan/vectorfield.mcd as a starting point and superimpose solutions to the vector fields so support your observation....
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