The complete integral of z=px +qy is
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Step-by-step explanation:
The given equation is : f(x,y,z,p,q)=px+qy+pq−z. So, Charpit's auxiliary equations are given by:
ds=
dp
0
=
dq
0
=
dz
z+pq
=
dx
x+q
=
dy
y+p
Now, from
ds=
dp
0
,ds=
dq
0
⟹p=C,q=D
being arbitray constants. Now, I have to use
dz=pdx+qdy=Cdx+Ddy
we get
z(x,y)=Cx+Dy+E
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