complementary function

For a nonhomogeneous linear differential equation a_ny⁽ⁿ⁾+a_n-1y⁽ⁿ⁻¹⁾+⋯+a_1y'+a_0y=g,…For a nonhomogeneous linear differential equation a_ny⁽ⁿ⁾+a_n-1y⁽ⁿ⁻¹⁾+⋯+a_1y'+a_0y=g(x), the general solution of the associated homogenous linear differential equation a_ny⁽ⁿ⁾+a_n-1y⁽ⁿ⁻¹⁾+⋯+a_1y'+a_0y=0.