The auxiliary equations is:
2y(z−3)dx=y(2x−z)dy=y(2x−3)dz
A first characteristic equation comes from
2y(z−3)dx=y(2x−3)dz
(2x−3)dx=2(z−3)dz
x2−3x+49=z2−6z+9+C1
(x−23)2=(z−3)2+C1
C1=(x−23)2−(z−3)2
A second characteristic equation comes from
y(2x−3−2x+z)dz−dy=2y(z−3)dx
2d(z−y)=dx
2(z−y)=x+C2
C2=2z−2y−x.
General solution of the PDE on the form of implicit equation:
Φ(C1,C2)=0
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