MATH 361 Exam 1, Spring 2002

Name:

1. Solve the equation:

y^{3} \frac{dy}{dx} = (y^{4} + 1) cos 5x

Ans: .

2. Solve the equation:

\frac{dy}{dx} + \frac{y}{x} = \frac{cos x}{x}, y(\frac{π}{2} ) = \frac{4}{π}

Ans: .

3. Solve the equation: [2x − y^{2} sin(xy)]dx + [cos(xy) − xy sin(xy) + 4]dy = 0

Name:

4. Sketch the solutions of y′ = y(16−y^{2}), y_{o} ≥ 0. Include the solution which satisfies the initial condition y(0) = 1/2 and \underline{write} a paragraph explaining how you got it. Classify the equilibrium solutions as asympotically stable, unstable or semistable.

5. A coke at room temperature of 70^{o}F is placed in a refrigerator with temperature 40^{o}F. After 10 min the coke is at 60^{o}F. When will the coke be at 45^{o}F?