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MATLAB 2

# MATLAB 2 - Exercise 2.1 Exercise 2.2 a y =(exp x y(exp x 1...

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Exercise 2.1 Exercise 2.2 a) -2 0 2 4 6 8 10 -4 -3 -2 -1 0 1 2 3 4 x y y ' = (exp( - x) - y) (exp( - x) + 1 + y)

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Dfield draws the lines based on the initial condition I provided when I clicked somewhere on the graph. b) It’s much easier to plot the direction field of a difficult or impossible differential than to actually solve it. Exercise 2.3 -2 0 2 4 6 8 10 -4 -3 -2 -1 0 1 2 3 4 x y y ' = x + y If the initial value in this problem weren’t (1,1) it wouldn’t greatly throw off the solution.
Exercise 2.4 -2 0 2 4 6 8 10 -4 -3 -2 -1 0 1 2 3 4 x y y ' = y - 2 It diverges quickly so inaccuracy throws off the solution greatly.

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Exercise 2.5 0 1 2 3 4 5 6 7 8 9 10 -4 -3 -2 -1 0 1 2 3 4 t y y ' = k (A - y) A = 1 k = 3 A is the ambient temperature because all solutions of the differential equation approach it

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