practice2

# practice2 - Midterm 2 Math 33B Practice Daniel Murfet May 8...

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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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## This note was uploaded on 09/20/2011 for the course MATH 33B 262223202 taught by Professor Dai during the Spring '09 term at UCLA.

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practice2 - Midterm 2 Math 33B Practice Daniel Murfet May 8...

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