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1.  The differential equation\(\frac{dy}{dt} = y^2 - y - 2\) has

a.  an unstable fixed point at \(y = 0\) and a stable fixed point at \(y = 2\).

b.  an unstable fixed point at \(y = 2\) and a stable fixed point at \(y = -1\).

c.  an unstable fixed point at \(y = -1\) and a stable fixed point at \(y = 2\).

d.  an unstable fixed point at \(y = 0\) and a stable fixed point at \(y = -1\).

e.  no fixed points.

2.  The differential equation\(\frac{dy}{dt} = y^2 - 2y + 1\) has

a.  has a stable fixed point at \(y = 0\).

b.  has an unstable fixed point at \(y = 0\).

c.  has a stable fixed point at \(y = 1\).

d.  has a fixed point at \(y = 1\) that is stable from below and unstable from above.

e.  has a fixed point at \(y = 1\) that is unstable from below and stable from above.

3.  The differential equation \(y'' + x^2y' - (\cos x)y - e^x = 0\)

a.  is first order and linear.

b.  is first order and non-linear.

c.  is second order and linear.

d.  is second order and non-linear.

e.  is third order and painted green.

4.  Which of the following is a solution to the differential equation \(y''+4y = 0\)?

a.  \(y(t) = e^t\)

b.  \(y(t) = e^{2t}\)

c.  \(y(t) = \sin t\)

d.  \(y(t) = \sin (2t)\)

e.  \(y(t) = \sin (4t)\)

5.  To be written out and submitted on Wednesday, January 29: Draw slope fields for the differential equations in questions 1 and 2. On each, sketch a few solution curves.