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G = g
e
x
l
+ 1
cos
2πvt
l
, f(x) = 0, F (x) =
1
7l
x
2
, 0 ≤ x ≤ l/4
1
63l
(x − l)
2
, l/4 ≤ x ≤ l
φ = g
vt
l
e
4πvt
l
ψ = 0
, F (x) = 0, f(x) =
(
x(x−
3l
8
)
h
, 0 ≤ x ≤ 3 l/8
0, 3l/8 ≤ x ≤ l
f(x) = T
|x−
l
2
|
l
sin
πx
l
.
f(x) = T
4(1 − cos
πx
l
) , 0 ≤ x ≤ l/6
9
25l
2
(1 −
√
3
2
)(x − l)
2
, l/6 ≤ x ≤ l
.
G = g
2x
2
l
2
+ e
x/l
, f(x) = (
x
l
− 1) sin
πx
2l
.
G = ge
2x
l
sin
πvt
l
, F (x) = 0, f (x) =
4l(1 − cos
πx
l
), 0 ≤ x ≤ l/7
49
9l
(1 − cos
π
7
)(x − l)
2
,l/7 ≤ x ≤ l
ψ = g
e
−πvt/2l
− e
πvt/2l
φ = 0
, f(x) = 0 , F (x) =
x(x−l)
h
cos
πx
2l
.
f(x) = T
x(l/8−x)
l
2
, 0 ≤ x ≤ l/8
0 , l/8 ≤ x ≤ l
.
f(x) = T
1
7l
2
x
2
, 0 ≤ x ≤ l/3
1
28l
2
(x − l)
2
, l/3 ≤ x ≤ l
.
G = g
1 − e
−
2x
l
, f(x) = T
(
0, 0 ≤ x ≤ l/8
(x−l)(
l
8
−x)
l
2
, l/8 ≤ x ≤ l
G = g
3x
2
l
2
−
x
l
cos
2πvt
l
, f(x) = 0, F (x) =
1
7l
x
2
, 0 ≤ x ≤ 2l/3
4
7l
(x − l)
2
,2l/3 ≤ x ≤ l
φ = g
vt
l
e
πvt
2l
ψ = 0
, F (x) = 0, f(x) =
(
0, 0 ≤ x ≤ 3l/8
(x−l)(x−
3l
8
)
h
, 3l/8 ≤ x ≤ l
f(x) = T
x−l
l
sin
πx
2l
.
f(x) = T
−
1
6
(1 − cos
πx
l
) , 0 ≤ x ≤ 2l/3
−
9
4l
2
(x − l)
2
, 2l/3 ≤ x ≤ l
.
G = g
x
l
−
6x
2
l
2
, f(x) =
x
l
sin
2πx
l
.
G = g
1 −
x
l
2
cos
3πvt
l
, F (x) = 0,f(x) =
2l(1 − cos
πx
l
), 0 ≤ x ≤ 2l/3
27
l
(x − l)
2
, 2l/3 ≤ x ≤ l
ψ = g
vt
l
e
−πvt/3l
φ = 0
, f(x) = 0 , F (x) = (x − l) sin
2πx
l
.
f(x) = T
0 , 0 ≤ x ≤ l/8
(x−l)(l/8−x)
l
2
, l/8 ≤ x ≤ l
.
f(x) = T
1
7l
2
x
2
, 0 ≤ x ≤ l/4
1
63l
2
(x − l)
2
, l/4 ≤ x ≤ l
.
G = g
x
l
− 1
, f(x) = T
x(x−3l/8)
l
2
, 0 ≤ x ≤ 3l/8
0 , 3l/8 ≤ x ≤ l
.
G = g
x
l
− 1
sin
2πvt
l
, f(x) = 0, F (x) =
4l(1 − cos
πx
l
),0 ≤ x ≤ 2l/3
54
l
(x − l)
2
, 2l/3 ≤ x ≤ l
φ = g
e
−
πvt
4l
− e
πvt
4l
ψ = 0
, F (x) = 0, f(x) =
(
0, 0 ≤ x ≤ l/4
(x−l)(
l
4
−x)
h
, l/4 ≤ x ≤ l
f(x) = T
x
l
sin
2πx
l
.
f(x) = T
4(1 − cos
πx
l
) , 0 ≤ x ≤ l/7
49
9l
2
(1 − cos
π
7
)(x − l)
2
, l/7 ≤ x ≤ l
.
G = g
x
l
+ 3
2
, f(x) = T
x(x−l)
l
2
cos
πx
2l
.
G = g
3x
2
4l
2
sin
3πvt
l
, F (x) = 0, f(x) =
(
4l(1 − cos
πx
l
), 0 ≤ x ≤ l/2
16(x−l)
2
l
, l/2 ≤ x ≤ l
ψ = g
v
2
t
2
l
2
e
πvt/4l
φ = 0
, f(x) = 0 , F (x) =
x
2
h
sin
πx
l
.
1 2
7l x , 0 ≤ x ≤ l/4 x 6x2 x
x
G = g e l + 1 cos 2πvt 3. G=g − , f (x) = sin 2πx
l .
4.
l , f (x) = 0, F (x) = 1 2 l l2 l
(x − l) , l/4 ≤ x ≤ l
63l 2l(1 − cos πx
x 2 3πvt l ), 0 ≤ x ≤ 2l/3
(
vt 4πvt
φ=g l e l x(x− 3l
8 )
, 0 ≤ x ≤ 3l/8 4. G =g 1− l cos l , F (x) = 0,f (x) = 27 2
5. , F (x) = 0, f (x) = h l (x − l) , 2l/3 ≤ x ≤ l
ψ=0 0, 3l/8 ≤ x ≤ l ψ = g vtl e−πvt/3l
5. , f (x) = 0 , F (x) = (x − l) sin 2πx
l .
φ=0
18
21
|x− 2l |
1. f (x) = T sin πx
l .
l
0, 0 ≤ x ≤ l/8
4(1 − cos√πxl ) , 0 ≤ x ≤ l/6 1. f (x) = T .
2. f (x) = T 9 3 2 . (x−l)(l/8−x)
, l/8 ≤ x ≤ l
25l2 (1
− 2 )(x − l) , l/6 ≤ x ≤ l 1 2
l2
x , 0 ≤ x ≤ l/4
2
2x
3. G = g
l2 + e
x/l
, f (x) = ( xl − 1) sin πx
2l . 2. f (x) = T 7l2
1 .
63l2 (x − l)2
, l/4 ≤ x ≤ l
4l(1 − cos πx
l ), 0 ≤ x ≤ l/7
2x
x(x−3l/8)
πvt , 0 ≤ x ≤ 3l/8
4. G = ge l sin
l , F (x) = 0, f (x) = 49 (1 − cos π )(x − l)2 ,l/7 ≤ x ≤ l x
3. G = g
l − 1 , f (x) = T .
l2
9l 7 0, 3l/8 ≤ x ≤ l
ψ = g e−πvt/2l − eπvt/2l
, f (x) = 0 , F (x) = x(x−l) 4l(1 − cos πx
5. cos πx
2l . x
2πvt l ),0 ≤ x ≤ 2l/3
4. G = g
l − 1 sin l , f (x) = 0, F (x) = 54 (x − l)2 ,
φ=0 h
2l/3 ≤ x ≤ l
πvt πvt
(l
19 φ=g e − 4l
− e 4l 0, 0 ≤ x ≤ l/4
5. , F (x) = 0, f (x) = (x−l)( 4l −x)
ψ=0 h , l/4 ≤ x ≤ l
x(l/8−x)
,
0 ≤ x ≤ l/8
1. f (x) = T l2 .
0, l/8 ≤ x ≤ l
1 2 22
2. f (x) = T 7l2 x , 0 ≤ x ≤ l/3
.
1 2
28l2 (x − l) , l/3 ≤ x ≤ l f (x) = T x 2πx
( 1.
l sin l .
0, 0 ≤ x ≤ l/8 4(1 − cos πx l ) , 0 ≤ x ≤ l/7
2x
3. G = g 1 − e− l , f (x) = T (x−l)( 8l −x) 2. f (x) = T 49 π 2 .
l2 , l/8 ≤ x ≤ l 9l2 (1 − cos 7 )(x − l) , l/7 ≤ x ≤ l
1 2 2
G = g xl + 3 , f (x) = T x(x−l) πx
7l x , 0 ≤ x ≤ 2l/3 cos(2l .
2
3x x 2πvt 3.
4. G = g
l2 − l cos l , f (x) = 0, F (x) =
l2
4 2
(x − l) ,2l/3 ≤ x ≤ l 4l(1 − cos πx
7l 2
l ), 0 ≤ x ≤ l/2
G = g 3x sin 3πvt
, F (x) = 0, f (x) =
(
πvt 4.
φ = g vtl e 2l 0, 0 ≤ x ≤ 3l/8 4l 2 l 16(x−l)2
, l/2 ≤ x ≤ l
5. , F (x) = 0, f (x) = (x−l)(x− 3l ) l
ψ=0 8
, 3l/8 ≤ x ≤ l 2 2
h ψ = g vl2t eπvt/4l x2
5. , f (x) = 0 , F (x) = h sin πx
l .
φ=0
20
1. f (x) = T x−l
l sin
πx
2l .
1
− 6 (1 − cos πxl ) , 0 ≤ x ≤ 2l/3
2. f (x) = T .
− 4l92 (x − l)2 , 2l/3 ≤ x ≤ l
25 26
