Prof. A. Suciu Name: depth2pt height-1.6pt width5truecm

MTH 1733 QUIZ 3 Fall 1997

• 6 points For each of the following curves, determine the equations of the asymptotes, if any:
  • $${y=\frac{2}{e^x-1}+3}$$
    
  • $${y=\ln (x^2 -4)}$$
    
  • $${y=e^{-\displaystyle{x^2}}}$$
  
  
• 6 points Differentiate the following functions:
  • $y=\displaystyle{x\sqrt{\ln x}}$
    
  • $y=\displaystyle{e^{\displaystyle{e^{x^2}}}}$
    
  • $y=\displaystyle{\frac{e^x+1}{x^e-1}}$
  
  

• 8 points Solve the following initial value problem:

  $$y''-9y=0,\quad y(0)=8,\quad y'(0)=2.$$

  
  
  
  

• 10 points For each of the following non-homogeneous differential equations with constant coefficients, write down the general form of the solution. You may leave the undetermined coefficients of the particular solution unevaluated, as in the following example.
  
  y'+y=2x+3 Solution:   y_h=C₁e^-x,  y_p=Ax+B,  y=y_h+y_p.
  
  • y'-3y=4x³-5x²
    
  • y'-3y=e^3x+x+3
    
  • y'-3y=2e^-3x-3e^2x
    
  • y''-y'=e^x
    
  • y''-y'=1