Matakuliah
Tahun
: D0024/Matematika Industri II
: 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
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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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first-order ODE of the form
(
5
)
can be solved by finding an integrating factor
(
6
)
(
7
)
Dividing through by
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yields
such that
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
(
1
0
)
But we can integrate both sides of (9) to obtain
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Now integrating both sides of (◇) gives
(with
now a known function), which can be solved for
to obtain
(
1
3
)
(
1
4
)
where
is an arbitrary constant of
integration.
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• Kerjakan latihan dalam modul soal
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