Prof. A. Suciu Name:

MTH 1733  QUIZ 3  Fall 1997

1. 6 points For each of the following curves, determine the equations of the asymptotes, if any:

(a) y = \frac{2}{e^{x} − 1} + 3

(b) y = ln(x^{2} − 4)

(c) y = e^{−x^{2}}

2. 6 points Differentiate the following functions:

(a) y = x\sqrt{ln x}

(b) y = ee^{x^{2}}

(c) y = \frac{e^{x} + 1}{x^{e} − 1}

MTH 1733  Quiz 3  Fall 1997

3. 8 points Solve the following initial value problem:

y′′ − 9y = 0, y(0) = 8, y′(0) = 2.

4. 10 points For each of the following non-homogeneous differential equations with constant coefficients, write down the \underline{general form} of the solution. You may leave the undetermined coefficients of the particular solution \underline{unevaluated}, as in the following example. y′ + y = 2x + 3 Solution: y_{h} = C_{1}e^{−x}, y_{p} = Ax + B, y = y_{h} + y_{p}.

(a) y′ − 3y = 4x^{3} − 5x^{2}

(b) y′ − 3y = e^{3x} + x + 3

(c) y′ − 3y = 2e^{−3x} − 3e^{2x}

(d) y′′ − y′ = e^{x}

(e) y′′ − y′ = 1