1. Matematika Pertemuan 11 Matakuliah : D0024/Matematika Industri II
Tahun : 2008
Matematika Pertemuan 11

2. Persamaan Diferensial Biasa
Bentuk Umum PDB adalah
                                
(1)
Bentuk Umum PDB linier adalah
Bila Q(x)=0 maka disebut PDB linier homogen
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3. Given a first-order ordinary differential equation
                    
(1)
if                 can be expressed using separation of variables as
                            
(2)
then the equation can be expressed as
                       
(3)
and the equation can be solved by integrating both sides to obtain
                              
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4. first-order ODE of the form
                           
(5)
can be solved by finding an integrating factor                     such that
    
                  
(6)
         
(7)
Dividing through by        yields
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5. for arbitrary and . To accomplish this, take
However, this condition enables us to explicitly determine the appropriate    
for arbitrary     and   . To accomplish this, take
                   
(9)
in the above equation, from which we recover the original equation (◇),
as required, in the form
                              
(10)
But we can integrate both sides of (9) to obtain
                  
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6. Now integrating both sides of (◇) gives
(with     now a known function), which can be solved for    to obtain
                              
(13)
                                                                 
(14)
where    is an arbitrary constant of integration.
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7. Kerjakan latihan dalam modul soal
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