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∆ := cos(
√
λ˜a −
√
λ
˜
b)
λ :=
π
2
(1 + 2 Z1 ˜)
2
4 (−
˜
b + ˜a)
2
λ :=
π
2
(1 + 2 k)
2
4 (−
˜
b + ˜a)
2
C1 sin
√
4
s
π
2
(1 + 2
˜
k)
2
(−
˜
b + ˜a)
2
x
4
+ C2 cos
√
4
s
π
2
(1 + 2
˜
k)
2
(−
˜
b + ˜a)
2
x
4
C1 :=
C2 cos(
π (1+2
˜
k) ˜a
2 (−
˜
b+˜a)
)
sin(
π (1+2
˜
k) ˜a
2 (−
˜
b+˜a)
)
C2 sin(
π ˜a−π x+2 π ˜a
˜
k−2 π x
˜
k
−2
˜
b+2 ˜a
)
sin(
π ˜a+2 π ˜a
˜
k
−2
˜
b+2 ˜a
)
Yn := (x,
˜
k) → sin(
π ˜a −π x + 2 π ˜a
˜
k −2 π x
˜
k
−2
˜
b + 2 ˜a
)
Ïðèðàâíèâàåì íóëþ ýòîò îïðåäåëèòåëü è ðåøàåì ïîëó÷åííîå õàðàêòåðè-
ñòè÷åñêîå óðàâíåíèå:
>Delta:=select(has,Delta,[cos]);
√ √
∆ := cos( λã − λb̃)
>_EnvAllSolutions:=true:lambda:=solve(Delta,lambda);
π 2 (1 + 2 _Z1 ˜)2
λ :=
4 (−b̃ + ã)2
>lambda:=subs(_Z1='k',lambda);
π 2 (1 + 2 k)2
λ :=
4 (−b̃ + ã)2
Íàõîäèì ñîáñòâåííûå ôóíêöèè:
>assume(k,posint):y(x);
s s
√ π 2 (1 + 2 k̃)2 √ π 2 (1 + 2 k̃)2
4 x 4 x
(−b̃ + ã)2 (−b̃ + ã)2
_C1 sin
+ _C2 cos
4 4
>C1:=solve(eq1,_C1);
_C2 cos( π2(1+2 k̃) ã
(−b̃+ã)
)
C1 :=
sin( π2(1+2 k̃) ã
(−b̃+ã)
)
>simplify(subs(_C1=C1,y(x))):combine(%);
_C2 sin( π ã−π x+2 π ã k̃−2 π x k̃
−2 b̃+2 ã
)
sin( π−2
ã+2 π ã k̃
b̃+2 ã
)
>Yn:=unapply(select(has,%,[x]),x,k);
π ã − π x + 2 π ã k̃ − 2 π x k̃
Yn := (x, k̃) → sin( )
−2 b̃ + 2 ã
Ïðîâåðèì äèôôåðåíöèàëüíîå óðàâíåíèå:
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