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MATH 20D hw2

# MATH 20D hw2 - Daisy Torres Math 20 D Moe Ebrahimi David...

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Daisy Torres Math 20 D Moe Ebrahimi  David Lipshutz B06 Thu 1:00 p.m. Exercise 2.1 a)  Sketch (by hand, without using MATLAB) the direction field of the following differential  equation:  dy/dx = -y/5 b)  On your direction field, add a curve that approximates the solution  passing through the point  = 0,  = 1.  -2 0 2 4 6 8 10 -4 -3 -2 -1 0 1 2 3 4 x y y ' = - y/5

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-2 0 2 4 6 8 10 -4 -3 -2 -1 0 1 2 3 4 t y y ' = - y/5 c)  >> dsolve ('Dy=-y/5')  ans =  C2/exp(t/5)
Exercise 2.2 a)   y' = (exp(-x) - y)*(exp(-x) + 2 + y) .  Now click in a few places on the plot.  What are the lines  which DFIELD has drawn?  Eenter the values x=2 and y=3.   -2 0 2 4 6 8 10 -4 -3 -2 -1 0 1 2 3 4 x y y ' = (exp( - x) - y) (exp( - x) + 2 + y)

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Exercise 2.3   Plot the direction field of  (dy/dx = x + 2y) .  Suppose that the experiment also reveals that the  initial value is about ( 0,1 ). Now click on points near ( 0,1 ) on the graph itself.  Using these plots,
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