complete integral of the equation z=px +qy - 2√pq is
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The given equation is : f(x,y,z,p,q)=px+qy+pq−z. So, Charpit's auxiliary equations are given by:
ds=dp0=dq0=dzz+pq=dxx+q=dyy+p
Now, from
ds=dp0,ds=dq0⟹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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