Solve dx/y-z =dy/z-x=dz/x-y
Answers
Answer:
The solution to the given system of equations is:
y = (3/4)x
z = (5/8)x
dy/dx = -3
dz/dx = (1/2)
Step-by-step explanation:
We can rewrite the given system of equations as:
dx/(y-z) = dy/(z-x) = dz/(x-y)
Let's assume a constant value k such that:
dx/(y-z) = k (1)
dy/(z-x) = k (2)
dz/(x-y) = k (3)
From equation (1), we get:
dx = k(y-z)
Substituting this value in equation (3), we get:
k(y-z)/(x-y) = k
Simplifying this equation, we get:
y-z = x-y
2y = 2x-z
y = x-(z/2) (4)
Similarly, substituting the value of dx and dy in equation (2), we get:
k(z-x)/(y-z) = k
Simplifying this equation, we get:
z-x = y-z
2z = x+y
z = (x+y)/2 (5)
Using equations (4) and (5), we can express y and z in terms of x:
y = x - (x+y)/4 = (3x-y)/4
4y = 3x
y = (3/4)x
z = (x+y)/2 = (5/8)x
Substituting these values in the original equations, we get:
dx/(y-z) = dx/[(3/4)x - (5/8)x] = dx/[(1/8)x] = 8dx/x
Similarly,
dy/(z-x) = dy/[(5/8)x - x] = dy/[(-3/8)x] = -(8/3)dy/x
dz/(x-y) = dz/[x - (3/4)x] = dz/[(1/4)x] = 4dz/x
Now, equating the first two terms, we get:
8dx/x = -(8/3)dy/x
24dx = -8dy
dy/dx = -3
Similarly, equating the first and third terms, we get:
8dx/x = 4dz/x
2dz = dx
dz/dx = (1/2)
Therefore, the solution to the given system of equations is:
y = (3/4)x
z = (5/8)x
dy/dx = -3
dz/dx = (1/2)
Learn more about similar questions visit:
https://brainly.in/question/30291290?referrer=searchResults
https://brainly.in/question/55112056?referrer=searchResults
#SPJ6