Question

solution of symmetric simultaneous de dx/x=dy/y=dz/z is

Answer 1

Answer:

So x,y,z are the multipliers. Therefore 1dx+1dy+1dz=0. Also xdx+ydy+zdz=0. I and II are the required solutions.

Answer 2

Given:

A simultaneous equation dx/x=dy/y=dz/z

Step-by-step explanation:

We solve it by Lagrange's multiplier.

(l(dx) + m(dy) + n (dz)/( lP + mQ +nR)=0 .

                     lP + mQ +nR = 0.

Then            ldx + mdy + ndz =0.

Here l,m,n are multipliers.

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

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

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

The multipliers are 1, 1,1

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

            x,y,z are the multipliers.

Hence          1dx + 1dy + 1dz=0.

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

Also xdx + ydy + zdz = 0.

After intégration x²+y²+z²=C2(Constant 2)              II

Answer = x+y+z=c1(constant 1) , x²+y²+z²=C2