Recall that a First Order Differential Equation of the form dy/dx = f(x, y) is called Homogeneous, provided f(x, y) is a Homogeneous Function of Degree Zero, i.e., f(λx, λy) = f(x, y) for any λ, x, y....

Recall that a First Order Differential Equation of the form

dy/dx = f(x, y)

is called Homogeneous, provided f(x, y) is a Homogeneous Function of Degree Zero, i.e.,

f(λx, λy) = f(x, y)

for any λ, x, y. Such equations can be transformed into Separable Equations by introducing a new unknown function v so that

y = xv

and by expressing dy/dx in terms of x, v and dv/dx.

Use this procedure to solve the homogeneous equation

dy/dx = (x^2 + 3xy + y^2) / x^2 , x > 0, y > 0.