Consider the differential equation y’(t)=2y(t)-3 and follow the steps below. a)Draw a direction field on the lines y=0,1,2,3 in the (t,y) plane for (1) b)include equilibrium solutions in the direction field and determine the behavior of y as t->infinity c)does this late-time behavior depend on the initial value of y at t=o? if so, describe the dependency.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the differential equation y’(t)=2y(t)-3 and follow the steps below.

a)Draw a direction field on the lines y=0,1,2,3 in the (t,y) plane for (1)

b)include equilibrium solutions in the direction field and determine the behavior of y as t->infinity

c)does this late-time behavior depend on the initial value of y at t=o? if so, describe the dependency.   

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