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f(x) = T
x(x−3l/8)
l
2
, 0 ≤ x ≤ 3l/8
0 , 3l/8 ≤ x ≤ l
.
f(x) = T
1
7l
2
x
2
, 0 ≤ x ≤ 2l/3
4
7l
2
(x − l)
2
, 2l/3 ≤ x ≤ l
.
G = g
3x
l
− e
−
x
l
, f(x) = T
(
0, 0 ≤ x ≤ 3l/8
(x−l)(x−
3l
8
)
l
2
, 3l/8 ≤ x ≤ l
G = g
2x
l
+ 4
cos
πvt
l
, f(x) = 0, F (x) =
(
−
3x
2
l
, 0 ≤ x ≤ l/3
−
3(x−l)
2
4l
, l/3 ≤ x ≤ l
φ = g
vt
l
e
−
πvt
l
− e
πvt
l
ψ = 0
, F (x) = 0, f (x) =
(
0, 0 ≤ x ≤ l/2
(x−l)(
l
2
−x)
h
,l/2 ≤ x ≤ l
f(x) = T
x(x−l)
l
2
cos
πx
2l
.
f(x) = T
−2(1 − cos
πx
l
) , 0 ≤ x ≤ 2l/3
−
27
l
2
(x − l)
2
, 2l/3 ≤ x ≤ l
.
G = g
x
2l
+ e
2x/l
, f(x) = (
x
l
− 1) sin
2πx
l
.
G = ge
−
2x
l
sin
2πvt
l
, F (x) = 0, f (x) =
(
4l(1 − cos
πx
l
), 0 ≤ x ≤ 3l/4
64(x−l)
2
l
(1 +
√
2
2
),3l/4 ≤ x ≤ l
ψ = g
e
πvt/l
− e
−πvt/2l
φ = 0
, f(x) = 0 , F (x) =
(x−l)
2
h
sin
πx
2l
.
f(x) = T
0 , 0 ≤ x ≤ 3l/8
(x−l)(x−3l/8)
l
2
, 3l/8 ≤ x ≤ l
.
f(x) = T
4(1 − cos
πx
l
) , 0 ≤ x ≤ 2l/3
54
l
2
(x − l)
2
, 2l/3 ≤ x ≤ l
.
G = g
e
x
2l
−
3x
2
4l
, f(x) = T
(
x(
l
4
−x)
l
2
, 0 ≤ x ≤ l/4
0, l/4 ≤ x ≤ l
G = ge
x
4l
sin
3πvt
l
, f(x) = 0, F (x) =
(
3x
2
l
, 0 ≤ x ≤ l/4
(x−l)
2
3l
, l/4 ≤ x ≤ l
φ = g
e
−
4πvt
l
− e
πvt
2l
ψ = 0
, F (x) = 0, f (x) =
(
x(
l
4
−x)
h
,0 ≤ x ≤ l/4
0, l/4 ≤ x ≤ l
23 Ñïèñîê ëèòåðàòóðû
x(x−3l/8)
, 0 ≤ x ≤ 3l/8 [1℄ Òèõîíîâ À.Í., Ñàìàðñêèé À.À. Óðàâíåíèÿ ìàòåìàòè÷åñêîé è-
1. f (x) = T l2 .
0, 3l/8 ≤ x ≤ l çèêè. Ì., Íàóêà, 1973
1 2
2. f (x) = T 7l2 x , 0 ≤ x ≤ 2l/3
.
4
2 (x − l)2
, 2l/3 ≤x≤l [2℄ Âëàäèìèðîâ Â.Ñ. Óðàâíåíèÿ ìàòåìàòè÷åñêîé èçèêè. Ì. Íàóêà,
7l
1971
(
3x − xl
0, 0 ≤ x ≤ 3l/8
3. G = g
l −e , f (x) = T (x−l)(x− 3l
8 )
l2 ( , 3l/8 ≤ x ≤ l [3℄ Àðàìàíîâè÷ È. ., Ëåâèí Â.È. Óðàâíåíèÿ ìàòåìàòè÷åñêîé èçè-
2
− 3xl , 0 ≤ x ≤ l/3 êè. Ì. Íàóêà, 1969
2x πvt
4. G = g
l + 4 cos l , f (x) = 0, F (x) = 3(x−l)2
−
( 4l
, l/3 ≤ x ≤ l [4℄ Î÷àí Þ.Ñ. Ìåòîäû ìàòåìàòè÷åñêîé èçèêè. Ì. Âûñøàÿ øêîëà,
1965
πvt πvt
vt
φ=g l e − l
−e l 0, 0 ≤ x ≤ l/2
5. , F (x) = 0, f (x) = (x−l)( 2l −x)
ψ=0 24 h ,l/2 ≤ x ≤ l [5℄ Êîøëÿêîâ Í.Ñ. è äð. Óðàâíåíèÿ â ÷àñòíûõ ïðîèçâîäíûõ ìàòåìà-
òè÷åñêîé èçèêè. Ì. Íàóêà, 1970
1. f (x) = T x(x−l) πx
l2 cos 2l . πx
−2(1 − cos l ) , 0 ≤ x ≤ 2l/3 [6℄ îäóíîâ Ñ.Ê. Óðàâíåíèÿ ìàòåìàòè÷åñêîé èçèêè. Ì. Íàóêà, 1971
2. f (x) = T .
− 27
l2 (x − l)2 , 2l/3 ≤ x ≤ l
x 2x/l
, f (x) = ( xl − 1) sin(2πx
3. G = g
2l + e l .
− 2x 2πvt 4l(1 − cos πx l ),
√
0 ≤ x ≤ 3l/4
4. G = ge l sin , F (x) = 0, f (x) = 64(x−l)2
l 2
l (1 + 2 ),3l/4 ≤ x ≤ l
πvt/l −πvt/2l
ψ=g e −e 2
5. , f (x) = 0 , F (x) = (x−l)h sin πx
2l .
φ=0
25
0, 0 ≤ x ≤ 3l/8
1. f (x) = T (x−l)(x−3l/8) .
l2 , 3l/8 ≤ x ≤ l
πx
4(1 − cos l ) , 0 ≤ x ≤ 2l/3
2. f (x) = T 54 2 .
l2 (x − l) , 2l/3 ≤ x ≤ l
(
x( 4l −x)
, 0 ≤ x ≤ l/4
x
3x2
3. G = g e 2l − 4l , f (x) = T l2
0, l/4 ≤ x ≤ l
(
3x2
x
G = ge sin 3πvt l , 0 ≤ x ≤ l/4
4.
l , f (x)
= 0, F (x) =
4l
(x−l)2
4πvt 3l( , l/4 ≤ x ≤ l
πvt x( 4l −x)
φ = g e− l − e 2l ,0≤ x ≤ l/4
5. , F (x) = 0, f (x) = h
ψ=0 0, l/4 ≤ x ≤ l
27 28
