Solve the homogeneous linear odes with constant coefficients: y" - 6y' + 8y = 0. m^2 - 6m + 8 = 0 (m - 2)(m - 4) m_1 = 2 m_2 = 4 y = c_1 e^2x + c_2 x e^4x y" - 6y' + 9y = 0. m^2 - 6m + 9 = 0 (m - 3)^2 = 0 m_1 = m_2 = 3 y = c_1 e^3x + c_2 x e^3x y" - 6y' 10y = 0. y"' + 3y" + 3y' + y = 0 y_1 = x^4 is a solution to the ode x^2 y" - 7xy' + 16y = 0, use reduction of order to find another independent solution.