Defination of Homogenous differential equation example and Method

Definition 

A differential equation is said to homogenous if it is written as

                   M(x,y)dx + N(x,y)dy=0 

Where   M(x,y and N(x,y) are homogenous function having same degree (homogenous)

FOR EXAMPLE

 f(x,y) = x^2 +xy +y^2 (homogenous function )

 g(x,y) = x^2y + y^3 + 1 

 1 constant is known as zero degree polynominal  

 h( x, y) = tan (x/y) + x^2 /y^2 

TO CHECK HOMOGENOUS

f (λx,λy) = λ^n f (x,y) 

               tan (λx/λy) + λ^2x^2 /λ^2y^2 

                 tan (x/y) + x^2/y^2 

 METHOD 

first check the degree of  M ( x,y) and N (x,y) if it is the same then put the y = Vx 

                      y= vx 

diff w.r.t "x" 

dy/dx = V+ xdv/dx 

This subtitude  reduces the equation to variable separable foam