(OL]DEHWK:RRG
       DIFFERENTIAL EQUATIONS AND INITIAL VALUE PROBLEMS
       
           EXAMPLE 2:    Solve the initial value problem. 
                                                  
           SOLUTION: 
           STEP 1: 
                                                      
           STEP 2: When x = -1, y = 0. 
                                                            
           EXAMPLE 3:    Solve the initial value problem. 
                                                
           SOLUTION: 
           STEP 1: 
                                               
           STEP 2: When t =  , s = 1. 
                                                  
           EXAMPLE 4:    Solve the initial value problem. 
                                                     
           SOLUTION: We will have to do the two steps twice to find the solution to this initial 
      Source URL: http://faculty.eicc.edu/bwood/math150supnotes/supplemental19.htm   
      Saylor URL: http://www.saylor.org/courses/ma102/                               
                                                                                     
      © Elizabeth Wood (http://faculty.eicc.edu/bwood/)                        Saylor.org 
      Used by Permission.                                                        2 of 5 
                    value problem. The first time through will give us y ' and the second time through will 
                    give us y. 
                    STEP 1: 
                                                                               
                    STEP 2: When x = 0, y ' = 4. 
                                                                
                    STEP 1: 
                                                                                              
                    STEP 2: When x = 0, y = 1. 
                                                                   
                    EXAMPLE 5:                Solve the initial value problem. 
                                                                                                                               
                    SOLUTION: Since we are working with the fourth derivative, we will have to go 
                    through the two steps four times.  
                    STEP 1: 
                                                                                           
                    STEP 2: When t = 0, y ''' = 7. 
                                                                                       
                    STEP 1: 
          Source URL: http://faculty.eicc.edu/bwood/math150supnotes/supplemental19.htm                                                                    
          Saylor URL: http://www.saylor.org/courses/ma102/                                                                                                
                                                                                                                                                          
          © Elizabeth Wood (http://faculty.eicc.edu/bwood/)                                                                                    Saylor.org 
          Used by Permission.                                                                                                                       3 of 5 
                                                      
           STEP 2: When t = 0, y '' = -1 
                                                      
           STEP 1: 
                                                        
           STEP 2: When t = 0, y ' = -1. 
                                                        
           STEP 1: 
                                                          
           STEP 2: When t = 0, y = 0. 
                                                   
           EXAMPLE 6:    Given the velocity, 
                                                        
                         and the initial position of the body as s (1/2) = 4. Find the body's 
                         position at time t. 
           SOLUTION: 
           STEP 1: 
                                           
      Source URL: http://faculty.eicc.edu/bwood/math150supnotes/supplemental19.htm   
      Saylor URL: http://www.saylor.org/courses/ma102/                               
                                                                                     
      © Elizabeth Wood (http://faculty.eicc.edu/bwood/)                        Saylor.org 
      Used by Permission.                                                        4 of 5