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

Persamaan Diferensial Biasa Bentuk Umum PDB adalah                                  (1) Bentuk Umum PDB linier adalah Bila Q(x)=0 maka disebut PDB linier homogen Bina Nusantara

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                                Bina Nusantara

first-order ODE of the form                             (5) can be solved by finding an integrating factor                     such that                         (6)           (7) Dividing through by        yields Bina Nusantara

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                    Bina Nusantara

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. Bina Nusantara

Kerjakan latihan dalam modul soal Bina Nusantara