 | In[3]:=
g = Expand[D[f[x], {x, 2}] -
2*x*D[f[x], x] + 8*f[x]]
Out[3]=
2*c + 8*e + 6*b*x + 6*d*x + 12*a*x^2 +
4*c*x^2 + 2*b*x^3
In[4]:=
Table[D[g, {x, k}], {k, 0, 3}]
Out[4]=
{2*c + 8*e + 6*b*x + 6*d*x + 12*a*x^2 +
4*c*x^2 + 2*b*x^3, 6*b + 6*d + 24*a*x +
8*c*x + 6*b*x^2, 24*a + 8*c + 12*b*x,
12*b}
In[5]:=
% /. b -> 0
% /. x -> 0
Out[5]=
{2*c + 8*e + 6*d*x + 12*a*x^2 + 4*c*x^2,
6*d + 24*a*x + 8*c*x, 24*a + 8*c, 0}
Out[6]=
{2*c + 8*e, 6*d, 24*a + 8*c, 0}
In[7]:=
Flatten[{a + b + c + d + e, %}];
% == {-(5/4), 0, 0, 0, 0}
% /. b -> 0
Solve[%, {a, b, c, d, e}]
Out[8]=
{a + b + c + d + e, 2*c + 8*e, 6*d,
24*a + 8*c, 0} == {-(5/4), 0, 0, 0, 0}
Out[9]=
{a + c + d + e, 2*c + 8*e, 6*d, 24*a + 8*c,
0} == {-(5/4), 0, 0, 0, 0}
Out[10]=
{{a -> 1, c -> -3, d -> 0, e -> 3/4}}
面白くないかも.
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