Pilihan Topik Matematika - at ee-cafe.org

209
Soal-Soal:
1. Carilah solusi persamaan diferensial berikut.
5
)
(0
0 ,
)
(0
0 ;
5
4
c).
10
)
(0
0 ,
)
(0
0 ;
4
4
b).
15
)
(0
0,
)
(0
0 ;
10
7
a).
2
2
2
2
2
2
=
=
=
+
+
=
=
=
+
+
=
=
=
+
+
+
+
+
+
+
+
dt
dv
v
v
dt
dv
dt
v
d
dt
dv
v
v
dt
dv
dt
v
d
dt
dv
v
v
dt
dv
dt
v
d
2. Carilah solusi persamaan diferensial berikut.
10
(0)
5,
)
(0
);
(
100
25
8
c).
10
(0)
5,
)
(0
);
(
100
25
10
b).
25
(0)
5,
)
(0
) ;
(
100
24
10
a).
2
2
2
2
2
2
=
=
=
+
+
=
=
=
+
+
=
=
=
+
+
+
+
+
dt
dv
v
t
u
v
dt
dv
dt
v
d
dt
dv
v
t
u
v
dt
dv
dt
v
d
dt
dv
v
t
u
v
dt
dv
dt
v
d
3. Carilah solusi persamaan diferensial berikut.
0
)
(0
0,
)
(0
,
)
(
]
100[cos1000
8
6
a).
2
2
=
=
=
+
+
+
+
dt
dv
v
t
u
t
v
dt
dv
dt
v
d
0
)
(0
0,
)
(0
,
)
(
]
100[cos1000
9
6
b).
2
2
=
=
=
+
+
+
+
dt
dv
v
t
u
t
v
dt
dv
dt
v
d
0
)
(0
0,
)
(0
) ,
(
]
100[cos1000
10
2
c).
2
2
=
=
=
+
+
+
+
dt
dv
v
t
u
t
v
dt
dv
dt
v
d