optimistДля
у меня получилось
Код:
In[22]:= f[x, y] := ky^4/(12 b^2) + (y^2 - b^2/4)^2*f[x]
D[f[x, y], x, x]
(-(b^2/4) + y^2)^2 (f^\[Prime]\[Prime])[x]
D[f[x, y], x, y]
Out[24]= (-(b^2/4) + y^2)^2 (f^\[Prime]\[Prime])[x]
In[26]:= 4 y (-(b^2/4) + y^2) Derivative[1][f][x]
D[f[x, y], y, y]
Out[26]= 4 y (-(b^2/4) + y^2) Derivative[1][f][x]
Out[27]= 8 y^2 f[x] + 4 (-(b^2/4) + y^2) f[x]
In[29]:= func =
1/(2 e) (((-(b^2/4) + y^2)^2 (f^\[Prime]\[Prime])[
x])^2 + (8 y^2 f[x] + 4 (-(b^2/4) + y^2) f[x])^2 -
2 nu (8 y^2 f[x] +
4 (-(b^2/4) + y^2) f[x]) ((-(b^2/4) + y^2)^2 (
f^\[Prime]\[Prime])[x])) +
1/(2 g) (4 y (-(b^2/4) + y^2) Derivative[1][f][x])^2
Out[29]= (8 y^2 (-(b^2/4) + y^2)^2 Derivative[1][f][x]^2)/g + 1/(
2 e)((8 y^2 f[x] + 4 (-(b^2/4) + y^2) f[x])^2 -
2 nu (-(b^2/4) + y^2)^2 (8 y^2 f[x] + 4 (-(b^2/4) + y^2) f[x]) (
f^\[Prime]\[Prime])[x] + (-(b^2/4) + y^2)^4 (f^\[Prime]\[Prime])[
x]^2)
In[30]:= phi = Integrate[func, {y, -b/2, b/2}]
In[31]:= (2 b^5 f[x]^2)/(5 e) + (b^7 Derivative[1][f][x]^2)/(
105 g) + (2 b^7 nu f[x] (f^\[Prime]\[Prime])[x])/(105 e) + (
b^9 (f^\[Prime]\[Prime])[x]^2)/(1260 e)
D[phi, f[x]]
Out[31]= (2 b^5 f[x]^2)/(5 e) + (b^7 Derivative[1][f][x]^2)/(
105 g) + (2 b^7 nu f[x] (f^\[Prime]\[Prime])[x])/(105 e) + (
b^9 (f^\[Prime]\[Prime])[x]^2)/(1260 e)
In[35]:= (4 b^5 f[x])/(5 e) + (2 b^7 nu (f^\[Prime]\[Prime])[x])/(
105 e)
D[phi, f'[x], x]
Out[35]= (4 b^5 f[x])/(5 e) + (2 b^7 nu (f^\[Prime]\[Prime])[x])/(
105 e)
In[37]:= (2 b^7 (f^\[Prime]\[Prime])[x])/(105 g)
D[phi, f''[x], x, x]
Out[37]= (2 b^7 (f^\[Prime]\[Prime])[x])/(105 g)
In[63]:= (2 b^7 nu (f^\[Prime]\[Prime])[x])/(105 e) + (b^9
\!\(\*SuperscriptBox[\(f\),
TagBox[
RowBox[{"(", "4", ")"}],
Derivative],
MultilineFunction->None]\)[x])/(630 e)
(4 b^5 f[x])/(5 e) + (2 b^7 nu (f^\[Prime]\[Prime])[x])/(105 e) - (
2 b^7 (f^\[Prime]\[Prime])[x])/(105 g) + (
2 b^7 nu (f^\[Prime]\[Prime])[x])/(105 e) + (b^9
\!\(\*SuperscriptBox[\(f\),
TagBox[
RowBox[{"(", "4", ")"}],
Derivative],
MultilineFunction->None]\)[x])/(630 e)
b := 1
e := 200*10^9
g := 8*10^10
k := 800*10^6
nu := 0.34
l := 5
(4 b^5 f[x])/(5 e) + (2 b^7 nu (f^\[Prime]\[Prime])[x])/(105 e) - (
2 b^7 (f^\[Prime]\[Prime])[x])/(105 g) + (
2 b^7 nu (f^\[Prime]\[Prime])[x])/(105 e) + (b^9
\!\(\*SuperscriptBox[\(f\),
TagBox[
RowBox[{"(", "4", ")"}],
Derivative],
MultilineFunction->None]\)[x])/(630 e)
Out[63]= 3.2381*10^-14 (f^\[Prime]\[Prime])[x] +
\!\(\*SuperscriptBox[\(f\),
TagBox[
RowBox[{"(", "4", ")"}],
Derivative],
MultilineFunction->None]\)[x]/126000000000000
Out[64]= f[x]/250000000000 - 1.73333*10^-13 (f^\[Prime]\[Prime])[x] +
\!\(\*SuperscriptBox[\(f\),
TagBox[
RowBox[{"(", "4", ")"}],
Derivative],
MultilineFunction->None]\)[x]/126000000000000
In[76]:= f[x]/250000000000 -
1.7333333333333332`*^-13 (f^\[Prime]\[Prime])[x] +
\!\(\*SuperscriptBox[\(f\),
TagBox[
RowBox[{"(", "4", ")"}],
Derivative],
MultilineFunction->None]\)[x]/126000000000000
DSolve[{f[x]/250000000000 -
1.7333333333333332`*^-13 (f^\[Prime]\[Prime])[x] +
\!\(\*SuperscriptBox[\(f\),
TagBox[
RowBox[{"(", "4", ")"}],
Derivative],
MultilineFunction->None]\)[x]/126000000000000 == 0, f[2.5] == 0,
f[-2.5] == 0, f'[2.5] == 0, f'[-2.5] == 0}, f[x], x]
Out[76]= f[x]/250000000000 - 1.73333*10^-13 (f^\[Prime]\[Prime])[x] +
\!\(\*SuperscriptBox[\(f\),
TagBox[
RowBox[{"(", "4", ")"}],
Derivative],
MultilineFunction->None]\)[x]/126000000000000
{{f[x] -> 0}}
Надо аппроксимировать теперь двумя модифицированными многочленами Чебышева?