1. Matematika Pertemuan 13 Matakuliah: D0024/Matematika Industri II Tahun : 2008

2. Bina Nusantara Persamaan Diferensial Eksak Consider a first-order ODE in the slightly different form (1) (1) Such an equation is said to be exact if (2) (2) This statement is equivalent to the requirement that a conservative field exists, so that a scalar potential can be defined. For an exact equation, the solution isconservative field (3) (3) where is a constant.

3. Bina Nusantara A first-order ODE ( ◇ ) is said to be inexact if (4) (4) For a nonexact equation, the solution may be obtained by defining an integrating factor of ( ◇ ) so that the new equation integrating factor (5) (5) satisfies (6) (6) or, written out explicitly,

4. Bina Nusantara This transforms the nonexact equation into an exact one. Solving the last equation for gives (8) (8) Therefore, if a function satisfying equation can be found, then writing (9) (9) (10) (10) in equation ( ◇ ) then gives (11) (11) which is then an exact ODE. Special cases in which can be found include -dependent, -dependent, and -dependent integrating factors.

5. Bina Nusantara Contoh-contoh Kerjakan latihan dalam modul soal