Question

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

Answer 1

Solution:

$2yzp+zxq=3xy$

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

$3ydy=zdz$

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

$xdx=2ydy$

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

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