Can you solve this differential equation

5√(xy) dy/dx = 4 x,y>0

Y=?

Could you plz solve this for me step by step? THanks.

Find the general solution by separating the variables then integrating:
5√(xy)(dy / dx) = 4
5√x√y(dy / dx) = 4
√y dy = 4 / (5√x) dx
∫ √y dy = 4 ∫ 1 / √x dx / 5
2√y³ / 3 = 8√x / 5 + C
√y³ = 12√x / 5 + C
y³ = (12√x / 5 + C)²
y = ₃√(12√x / 5 + C)²

5√(xy) (dy/dx) = 4x

dy/dx = 4/5 * √x/√y

5/4 * √y dy = √x dx

Integrating both sides:

5/6 * y^(3/2) = 2/3*x^(3/2) + C

5√(xy) dy/dx = 4 x,y>0

5√(y) dy/dx = 4 x/x^1/2 = 4x^1/2

5y^1/2 dy = 4x^1/2 dx

[10/3] y^3/2 = [ 8/3 ]x^3/2 +c

5 √x √y dy/dx = 4x
5√y dy = 4√x dx
5 y^(3/2)/(3/2) = 4x^(3/2)/(3/2) + C

5/4 (y/x)^(3/2) = C
(5/4)x^(3/2) = Cy^(-3/2)
y^(3/2) = C (4/5) x^(-3/2)
y = (4/5)^(2/3) x^(-1) + C