Ujian Sisipan 2 Semester Pendek FMIPA USU 2008


Mata Kuliah : Persamaan Diferensial Elementer
Tanggal : Senin, 22 Agustus 2005
Dosen : Sumardi
Sifat : Close
1. Cari masalah nilai awal berikut dengan menggunakan tranformasi laplace
d 2 y
dx2 −
dy
dx−2y=18 e−t sin3t
y(0) = 0 , y'(0) = 3
2. Tentukan solusi deret pangkat masalah syarat awal berikut :
 x3−1
d 2 y
dx2 x2 dy
dxxy=0
y(0) = 2 , y'(0) = -2
3. Cari penyelesaian umum sistem persamaan diferensial linear homogen :
dx
dt =3x−y
dy
dt =4x−y
4. Diketahui pasangan x(t) dan y(t) merupakan solusi sistem PD :
2 dx
dt dy
dt −x−y=e−t
dx
dt dy
dt 2xy=et
Dengan syarat awal x(0) = 2 dan y(0) = 1, tentukan y(t)!
Tabel Laplace:
L{eat }= 1
s−a
; L{sinbt }= b
s2b2 ; L{cosbt }= s
s2b2 ; L{tn}= n!
sn1
L {sinhbt }= b
s2−b2 ; L{coshbt }= s
s2−b2
http://himatika.mipa.ugm.ac.id
re-write by Zaki , http://zaki.web.ugm.ac.id

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