Homogeneous Equations:

A differential equation of the form

 
 Where g (x, y) and ƒ (x, y) are homogeneous functions of y and x of the similar degree is known as homogeneous differential equation.

If ƒ (x, y) and g (x, y) are homogeneous functions of degree n each, then we may write

ƒ (x, y) = xⁿ ƒ₁ (y/x) and g (x, y) = xⁿ g₁ (y/x).

Now (i) takes the form

 
 To compute that equation, we put y = Vx, where V is a function of x.

Differentiating y = Vx w.r.t.  x,

 
 Replacing in (ii), we obtain

 
 which being a differential equation with different variables may be computed.