practice2 - Midterm 2 Math 33B - Practice Daniel Murfet May...

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Daniel Murfet May 8, 2011 Q. Consider the differential equation y 0 = ( y + 2) 2 ( y - 1). (a) Sketch f ( y ) = ( y + 2) 2 ( y - 1) as a function of y . (b) Find all equilibrium solutions of the differential equation. (c) Draw the phase line for the given differential equation and describe each equilibrium as asymptotically stable or unstable. (d) On one graph, sketch the equilibrium solutions and one solution curve in each of the regions into which the equilibrium solutions divide the plane. Q. Which of the following pairs of functions give fundamental sets of solutions to the equation y 00 + y 0 + y = 0? (There may be none, one, or more than one.) For those pairs which are not solutions, explain very briefly why this is the case. e - 1 2 t cos( 3 2 t ) ,e - 1 2 t sin( 3 2 t ). e - 1 2 t cos( 3 2 t ) ,e - 1 2 t . e - 1 2 t cos( 3 2 t ) ,e - 1 2 t sin( t ). 2
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practice2 - Midterm 2 Math 33B - Practice Daniel Murfet May...

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