1. Draw the direction field for the differential equations (a) y' = 3- 2y; (b) y...

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1. Draw the direction field for the differential equations (a) y' = 3- 2y; (b) y = y(4 - y); and (c) y' = et + y (10 pts) 2. Create a differential equation that does not possess any real solutions. (10 pts) 3. Make up a differential equation that you feel confident possesses only the trivial solution y = 0. Explain your reasoning. (10 pts) 4. What function do you know from calculus is such that its first derivative is itself? Its first derivative is a constant multiple k of itself? Write each answer in the form of a first-order differential equation with a solution. (5 pts) 1. Draw the direction field for the differential equations (a) y' = 3- 2y; (b) y = y(4 - y); and (c) y' = et + y (10 pts) 2. Create a differential equation that does not possess any real solutions. (10 pts) 3. Make up a differential equation that you feel confident possesses only the trivial solution y = 0. Explain your reasoning. (10 pts) 4. What function do you know from calculus is such that its first derivative is itself? Its first derivative is a constant multiple k of itself? Write each answer in the form of a first-order differential equation with a solution. (5 pts)

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