The main focus of this paper is that in which the nonlinearity does not occur in the highest differentiated term.This paper will further discuss one observed method. The method to be presented has the..
The main focus of this paper is that in which the nonlinearity does not occur in the highest differentiated term.This paper will further discuss one observed method. The method to be presented has the particular advantage that its wide scope and application, yet it is constrained to differential equations that are associated with nonconservative systems.We wish to extend the results of [2] to all real numbers in the domain of x. The Ermakov-Pinney method of lineraization was employed to obtain solvable form of the equation. An implicit solution of the nonlinear differential equation y00 + P(x)y = qm(x)=ym is found to be y = jw[(C1 R dx w2 + C2)2 + C3]j 1 1ōmjj + C4 if qm(x) = w(x)mō3. Where w is the combination of two linearly independent solutions u and v, such the w(x) = au(x) + bv(x), as well as ' = R w(x)ō2dx. Where C1,C2,C3, and C4 are arbitrary constants.
