Section 4.5  Homogeneous Linear Equations with Constant Coefficients

• to be able to use auxiliary equations to derive general solutions
• to be able to solve homogeneous linear equations with constant coefficients with initial conditions
• to be able to use auxiliary equations when there are repeated roots
• to be able to solve Cauchy-Euler equations

• auxiliary equations

 
• distinct vs. repeated roots

 
• Cauchy-Euler equations

 

• development of auxiliary equations

 

 
 
 
 
 
 
 
 
 
 
 
 

• using auxiliary equations, #1,10 (repeated roots),12 (quadratic formula)

 

 
 
 
 
 
 
 
 
 
 
 
 
 

• solving given initial value problem, #19

 

 
 
 
 
 
 
 
 
 
 
 
 

• finding solution to third order differential equation, #27

 

 
 
 
 
 
 
 
 
 
 
 
 

• finding general solution to Cauchy-Euler equations, #33

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• using the calculator to obtain solutions, #49a

 

 
 
 
 
 
 
 
 
 
 

QUESTION OF THE DAY

Evaluate

SOLUTION