Question

Find the general solution of the Lagrange's equation 2yzp + zxq = 3xy

Answer 1

$\frac{dx}{2yz}=\frac{dy}{zx}=\frac{dz}{3xy}$

$3ydy=zdz$

$3y^2-z^2=c_1$

$xdx=2ydy$

$x^2-2y^2=c_2$

$F(c_1,c_2)=F(3y^2-z^2,x^2-2y^2)=0$