Question

Solution of symmetric simultaneous DE DX/y = dy/x = dz/xz is​

Answer 1

Step-by-step explanation:

This is a simultaneous Total Differential equation.

We solve it by Lagrange's multiplier.

(ldx+mdy +n dz)/(lP+mQ+nR)=0 .

lP+mQ+nR = 0. So ldx+mdy+ndz =0.

Here l,m,n are multipliers.

dx/y-z =dy/z-x =dz/x-y given.

So. 1dx +1dy +1dz =0.Since.

1(y-z)+1(z-x)+1(x-y)=0,

1, 1,1 are the multpliers.

And x(y-z)+y(z-x)+z(x-y)= 0.

So x,y,z are the multipliers.

Therefore 1dx+1dy+1dz=0.

After intégration x+y+z=c1(constant 1). I

Also xdx+ydy+zdz=0.

After intégration x^2+y^2+z^2=C2(Constant 2).II

I and II are the required solutions.