Homogeneous Equations. The differential equation. is homogeneous if the function f(x,y) is homogeneous, that is-. Check that the functions. . are homogeneous. In order to solve this type of equation we make use of a substitution (as we did in case of Bernoulli equations). Indeed, consider the substitution . If f(x,y) is homogeneous, then we have. Since y' = xz' + z, the equation (H) becomes. which is a separable equation.