[과제 5 : 2장 7, 10절, 3장 3절]
1. Consider the ODEs ″′   ″   ′       ---(*).
(1) Find the general solution   of ″′   ″   ′    .
(2) The table represents the choice of   for each    in (*). Find all the good choices of  
when the method of undetermined coefficients is used.

  

(1) 
(2)   
(3)  
(4)      
(5) sin 

correct what’s wrong


 
  
         
 sin 
2. If      cos    sin        (  and  are arbitrary constants) is the general
solution of  ″   ′       , then  

, 

, and    

.
3. Write a trial solution of   when we use the method of undetermined coefficients. Do not
determine the coefficients.
(1) ″′  ″  ′       sin .     
(2)  ″   ′   cos .     


(3) ″  ′        sin     .     

(4)  ″   ′      .     

(5)  ″   ′           .     

(6)     ″′       .     

(7)    ″      sin  .     

4. Find a particular solution of  ″   ′      .    

.
5. Use the method of undetermined coefficients to find the general solution of the following
non-homogeneous second order linear ODE:  ″   ′         ∞    ∞ .


6. (1) A solution of  ″    ′  
      is      . Then a second solution   , which is


linearly independent of   , is     



(2) A particular solution   of the non-homogeneous linear ODE  ″    ′  
      is


   

   

   .
7. Find a particular solution   of the ODE    ″       ′            .
8. The equation  ″      ′       has a solution       on the interval  ∞ .
(1) Find the second solution           .
(2) Show that   and  is the basis for the general solution of ODE, using the Wronskian.
(3) Use the method of variation of parameters to find a general solution of the ODE:
 ″      ′        
9. Solve the ODEs

(1)  ″   ′    
  

(2)  ″   ′    

(3)    ″   ′    ln     
(4)    ″   ′       
ln 
(5)  ″   ′      

(6)  ″′   ′         sin 