I'm not sure what you mean by "two conjugate roots as solution to 4th order ode". Perhaps you mean two conjugate roots of the characteristic equation of the ode? But then I don't know what you mean by "the two roots are proportional". The characteristic equation of a 4th order ode is a fourth degree polynomial equation which generally has four roots. Just knowing two of the roots is not enough to tell you all four independent solutions. Or do you mean that two solutions are conjugates and there exist a second pair that are proportional to the first?