Abstarct: Linear and non-linear differential equations appear in many engineering problems. al-though many of these problems can be solved using analyticaland numerical methods, but there is another problems that can be solved using analytical and numerical or not resolved, or to solve complex. hence the semi-analytical methods can be a good alternative to solve this problems, in this dissertation we try to second order non-linear equations to solve adomian decomposition method however, about this adomian decomposition method can be said that this method solution to obtain an infinite series that converges to the real answer, in the end we try the method in the form bring up to format calculus quantum.