Solution:

Given, Y= √(x/m) √(m/x)

Let's simplify the equation first.

Y = √(x/m) √(m/x)
Y = √(x/m) * √(m/x) (product of square roots = square root of product)
Y = √(x/m * m/x)
Y = √(1)
Y = 1

So, Y is a constant value of 1.

Next, we need to find 2xy dy/dx - x/m m/x

Let's differentiate Y = √(x/m) √(m/x) with respect to x.

Y = √(x/m) * √(m/x)
Y = (x/m)^(1/2) * (m/x)^(1/2)
Y = x^(1/2) * m^(-1/2) * m^(1/2) * x^(-1/2)
Y = 1

Now, differentiating Y with respect to x.

dY/dx = 0

Now, let's differentiate Y = √(x/m) √(m/x) with respect to y.

Y = √(x/m) * √(m/x)
Y = x^(1/2) * m^(-1/2) * m^(1/2) * x^(-1/2)
Y = 1

Now, differentiating Y with respect to y.

dY/dy = 0

Using the chain rule, we can find dy/dx.

dY/dx = dY/dy * dy/dx

0 = dY/dy * dy/dx

dy/dx = 0/dY/dy

dy/dx = 0

Now, let's find 2xy dy/dx - x/m m/x

2xy dy/dx - x/m m/x = 2xy * 0 - x/m * m/x
2xy dy/dx - x/m m/x = -1

Therefore, 2xy dy/dx - x/m m/x = -1.

Y = sqrt(x/m) * sqrt(m/x)