Решите дифференциальное уравнение
(sqrt(x*y)-sqrt(x))*dx+(sqrt(x*y) sqrt(y))*dy=0

The given equation is:

(sqrt(x*y) - sqrt(x))*dx + (sqrt(x*y) sqrt(y))*dy = 0

To solve this equation, we can rearrange it and separate the variables:

(sqrt(x*y) - sqrt(x))dx = - (sqrt(x*y) sqrt(y))dy

Divide both sides of the equation by sqrt(y) and dx:

(sqrt(x)/sqrt(y) - 1/sqrt(y)) dx = - sqrt(x) dy

Now, we can integrate both sides of the equation with respect to their respective variables:

∫(sqrt(x)/sqrt(y) - 1/sqrt(y)) dx = - ∫sqrt(x) dy

To integrate the left side with respect to x, we treat sqrt(y) as a constant:

(sqrt(y)/sqrt(y)) * ∫sqrt(x) dx - (1/sqrt(y)) * ∫dx = - ∫sqrt(x) dy

Simplifying the integrals:

∫sqrt(x) dx - (1/sqrt(y)) * x = - ∫sqrt(x) dy

Integrating both sides:

(2/3) x^(3/2) - (x/sqrt(y)) = - (2/3) y^(3/2) + C

Where C represents the constant of integration. This is the general solution to the given equation.