Web viewtugas 5. mata kuliah: “kalkulus lanjut” dosen pengampuh. prof.dr.p. siagian,...
Transcript of Web viewtugas 5. mata kuliah: “kalkulus lanjut” dosen pengampuh. prof.dr.p. siagian,...
Tugas 5
MATA KULIAH:
“KALKULUS LANJUT”
DOSEN PENGAMPUH
Prof.Dr.P. Siagian, M.Pd
NAMA: HERI RISDIANTONIM : 8106172005
PENDIDIKAN MATEMATIKAPASCA SARJANA
UNIVERSITAS NEGERI MEDAN2010
1 . y ''+9( y )=0 , y (0 )= 3, y'(0 )= -5
Jawab
L (y’’+9(y)) = L (0) L (y’’)+ L (9(y)) = L (0)
s2(y(s)) – s y(0) – y’(0) + 9 y(s)=0
s2(y(s)) –3s –5 +9 y(s) = 0
s2(y(s)) +9 y(s) = 3s +5
y(s)(s2 + 9) = 3s + 5
y ( s )=3 s+5s2+9
y ( t )= L -1
( 3 s+5s2+9 )
y ( t )= L -1
( 3 ss2+9 ) +L -1
( 5s2+9 )
y(t) = 3 cos3t + 5 sin3t
2 . y ''−3 y '+4 y=0 , y( 0)= 1, y'(0 )= 5
Jawab
L (y’’- 3(y) + 4y) = L (0) L (y’’)- L (3y’)+ L 4y= L (0)
s2(y(s)) – s y(0) – y’(0) – 3(s y(s) - y (0))+ 4 y(s)=0
s2y(s) – s – 5 – 3 s y(s) +3 + 4y(s) = 0
s2y(s)– 3 s y(s) + 4y(s) = s + 2
y(s)(s2 – 3 s + 4)= s + 2
y ( s )= s+2s2−3 s+4
y ( t )= L -1
( s+2s2−3 s+4 )
y ( t )= L -1
( ss2−3 s+4 ) +L -1
( 2s2−3 s+4 )
y ( t )= L -1
( s−32
( s−32)2+7
4) +L -1
(3
2
( s−32)2+7
4) +L -1
( 2
( s−32)2+7
4 )y ( t )=
L -1
( s−32
( s−32)2+7
4) +
(7
2
( s−32)2+7
4)
y ( t )=e3
2 cos √ 74 t+ 7
2 e3
2 sin√ 74 t
3 .d2 qdt 2 +8 dq
dt+25 q=30 sin 2t ; q(0 )=q ' (0 )=0
Jawab
L ( d2 q
dt2 +8 dqdt
+25 q )= L (30 sin 2t )
L (y’’)- L (3y’)+ L 4y= L (0)
s2(y(s)) – s y(0) – y’(0) – 3(s y(s) - y (0))+ 4 y(s)=0
s2y(s) – s – 5 – 3 s y(s) +3 + 4y(s) = 0
s2y(s)– 3 s y(s) + 4y(s) = s + 2
y(s)(s2 – 3 s + 4)= s + 2
y ( s )= s+2s2−3 s+4
y ( t )= L -1
( s+2s2−3 s+4 )
y ( t )= L -1
( ss2−3 s+4 ) +L -1
( 2s2−3 s+4 )
y ( t )= L -1
( s−32
( s−32)2+7
4) +L -1
(3
2
( s−32)2+7
4) +L -1
( 2
( s−32)2+7
4 )y ( t )=
L -1
( s−32
( s−32)2+7
4) +
(7
2
( s−32)2+7
4)
y ( t )=e3
2 cos √ 74 t+ 7
2 e3
2 sin√ 74 t