In[]:=
e=Expand[
4
F[z]
(0,4)
f
[y0,z]+
2
F[z]
3y0
2
′′
F
[z]
2
(1,0)
f
[y0,z]+y0
(2,0)
f
[y0,z]+4y0
′
F
[z]
(3)
F
[z]2
(1,0)
f
[y0,z]+y0
(2,0)
f
[y0,z]+12y0
′
F
[z]
′′
F
[z]2
(1,1)
f
[y0,z]+y0
(2,1)
f
[y0,z]+2
(2,2)
f
[y0,z]+6y0
2
′
F
[z]
2
(1,2)
f
[y0,z]+y0
(2,2)
f
[y0,z]+
(4,0)
f
[y0,z]+2
2
′
F
[z]
6
(2,0)
f
[y0,z]+6y0
(3,0)
f
[y0,z]+
2
y0
(4,0)
f
[y0,z]+y0
4
′
F
[z]
24
(1,0)
f
[y0,z]+36y0
(2,0)
f
[y0,z]+12
2
y0
(3,0)
f
[y0,z]+
3
y0
(4,0)
f
[y0,z]y0
3
F[z]

(4)
F
[z]
(1,0)
f
[y0,z]+4
(3)
F
[z]
(1,1)
f
[y0,z]+6
′′
F
[z]
(1,2)
f
[y0,z]+4
′
F
[z]
(1,3)
f
[y0,z]+2F[z]
′′
F
[z]2
(2,0)
f
[y0,z]+y0
(3,0)
f
[y0,z]+3y0
2
′
F
[z]
′′
F
[z]6
(1,0)
f
[y0,z]+6y0
(2,0)
f
[y0,z]+
2
y0
(3,0)
f
[y0,z]+2
′
F
[z]2
(2,1)
f
[y0,z]+y0
(3,1)
f
[y0,z]+2y0
3
′
F
[z]
6
(1,1)
f
[y0,z]+6y0
(2,1)
f
[y0,z]+
2
y0
(3,1)
f
[y0,z]]
Out[]=
4
F[z]
(0,4)
f
[y0,z]+24y0
4
′
F
[z]
(1,0)
f
[y0,z]+6y0
2
F[z]
2
′′
F
[z]
(1,0)
f
[y0,z]+8y0
2
F[z]
′
F
[z]
(3)
F
[z]
(1,0)
f
[y0,z]+24y0
2
F[z]
′
F
[z]
′′
F
[z]
(1,1)
f
[y0,z]+12y0
2
F[z]
2
′
F
[z]
(1,2)
f
[y0,z]+12
2
′
F
[z]
(2,0)
f
[y0,z]+36
2
y0
4
′
F
[z]
(2,0)
f
[y0,z]+3
2
y0
2
F[z]
2
′′
F
[z]
(2,0)
f
[y0,z]+4
2
y0
2
F[z]
′
F
[z]
(3)
F
[z]
(2,0)
f
[y0,z]+12
2
y0
2
F[z]
′
F
[z]
′′
F
[z]
(2,1)
f
[y0,z]+2
2
F[z]
(2,2)
f
[y0,z]+6
2
y0
2
F[z]
2
′
F
[z]
(2,2)
f
[y0,z]+12y0
2
′
F
[z]
(3,0)
f
[y0,z]+12
3
y0
4
′
F
[z]
(3,0)
f
[y0,z]+
(4,0)
f
[y0,z]+2
2
y0
2
′
F
[z]
(4,0)
f
[y0,z]+
4
y0
4
′
F
[z]
(4,0)
f
[y0,z]36y0F[z]
2
′
F
[z]
′′
F
[z]
(1,0)
f
[y0,z]+y0
3
F[z]
(4)
F
[z]
(1,0)
f
[y0,z]+24y0F[z]
3
′
F
[z]
(1,1)
f
[y0,z]+4y0
3
F[z]
(3)
F
[z]
(1,1)
f
[y0,z]+6y0
3
F[z]
′′
F
[z]
(1,2)
f
[y0,z]+4y0
3
F[z]
′
F
[z]
(1,3)
f
[y0,z]+4F[z]
′′
F
[z]
(2,0)
f
[y0,z]+36
2
y0
F[z]
2
′
F
[z]
′′
F
[z]
(2,0)
f
[y0,z]+8F[z]
′
F
[z]
(2,1)
f
[y0,z]+24
2
y0
F[z]
3
′
F
[z]
(2,1)
f
[y0,z]+2y0F[z]
′′
F
[z]
(3,0)
f
[y0,z]+6
3
y0
F[z]
2
′
F
[z]
′′
F
[z]
(3,0)
f
[y0,z]+4y0F[z]
′
F
[z]
(3,1)
f
[y0,z]+4
3
y0
F[z]
3
′
F
[z]
(3,1)
f
[y0,z]
In[]:=
Coefficient[e,
(1,1)
f
[y0,z]]
Out[]=
0