what is the solution of dx/y=dy/x=dz/z ?
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Answered by
2
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
Answered by
3
Step-by-step explanation:
x^2+y^2+z^2=(2) (Constant 2)
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