1 0. dy/dx=(4y - 3x)/(2x - y) (2x - y)dx - (4y - 3x)dy = 0. If you multiply x and y by a scalar, say A, you get. (2Ax - Ay)dx - (4Ay - 3Ax)dy = A(2x - y)dx - A(4y - 3x)dy. = A[(2x - y)dx - (4y - 3x)dy] = 0. Since this scales the whole left hand side by A, the equation is homogeneous. In general: A polynomial P(v) with all terms having degree n is homogeneous as P(Av) = A n P(v) for all vectors v and scalars A. A differential equation of the form dy/dx = M(x,y) / N(x,y) is homogeneous if M and N are homogeneous of the same degree. Proof: Let M and N be both homogeneous polynomials of degree K. Rewrite M(x,y) dx - N(x,y) dy = 0