hw1 - ODE, Homework 1 Due June 2, 2008 1. Draw a reasonably...

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Unformatted text preview: ODE, Homework 1 Due June 2, 2008 1. Draw a reasonably detailed direction field for y = y + t . Sketch 3 solutions with different behaviors. Are there any equilibrium solutions? Are there any asymptotic solutions? If so, what are they? 2. Sketch a direction field for y = sin( y ). Sketch at least 3 equilibrium solutions and at least 4 others with different behavior. What are the equilibrium solutions? What are their stabilities? At what values of y do the solutions have inflection points? 3. Write down a differential equation of the form y = ay + b for a, b R such that they have the required behavior as t : a) all solutions approach y = 26, b) all non-equilibrium solutions diverge from u = 117 / 29. 4. Write down a differential equation such that as t , all solutions approach the line y = 2 t . 5. (2.5.28 from text) Chemical reactions. A second order chemical reaction involves the in- teraction (collision) of one molecule of a substance P with one molecule of a zubstance...
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This note was uploaded on 10/18/2011 for the course MATH S3027D taught by Professor Peters during the Spring '11 term at Columbia.

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hw1 - ODE, Homework 1 Due June 2, 2008 1. Draw a reasonably...

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