Answer to Question #151701 in Differential Equations for Sumo

Question

z(x + y) p+z(x -y)q=x^2+y^2 , where p=dz/dx ,q=dz/dy

Answer 1

P=z(x+y)=zx+yz

Q=z(x-y)=zx-zy

R=x²+y²

$\frac{dx}{zx+yz}=\frac{dy}{zx-zy}=\frac{dz}{x^2+y^2}$

Multiplyers x,-y,-z

xdx-ydy-zdz=0

1/2(x²-y²-z²)=C₁

Multiplyers -x,y,z

-xdx+ydy+zdz=0

1/2(-x²+y²+z²)=C₂