A function f(x,y) is homogeneous of degree n if f(tx,ty) = $t^n$ * f(x,y). A DE dy/dx = f$\frac{x,y}{g}$(x,y) is homogeneous if both f and g are homogeneous of the same degree. Equivalently, dy/dx can be written as a function of y/x alone. Method: substitute y = vx, so dy/dx = v + x*dv/dx. Replace and simplify to get a separable equation in v and x. After solving for v(x), substitute back v = $\frac{y}{x}$. Quick check for homogeneity: every term in the equation should have the same total degree when you count powers of x and y. For example, ($x^2$ + xy) dy = ($y^2$ + xy) dx has all terms of degree 2. But $x^2$ + y does NOT have uniform degree, so it's not homogeneous.