Section 4.6  Auxiliary Equations with Complex Roots

• to be able to use auxiliary equations with complex roots to derive solutions
• to be able to solve initial value problems
• to be able to solve Cauchy-Euler equations

• Euler's formula

 
• derivative of e^ix   
  
  
• derivatives of complex functions
  
  
• real solutions derived from complex solutions
  
  

• finding general solutions when the auxiliary equation has complex roots, #4
  
  
  
  
  
  
  
  
  
  
• solving initial value problem, #23 (two ways if there is time)
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• higher order equations, #29b  (use calculator)
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• finding a general solution to a Cauchy-Euler equation,#33
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• vibrating spring with and without damping, #36,37
  
  
  
  
  
  
  
  
  
  

QUESTION OF THE DAY

Find  ..

SOLUTION