Close-to-convex Function Generates Remarkable Solution of 2^nd order Complex Nonlinear Differential Equations

Consider the complex nonlinear differential equation ( ) ( ) ( ) ( ) where ( ) ( ) are complex coefficients, and ( ) be a complex function performs nonhomogeneous term of given equation. In this paper, we investigated that ( ) is a remarkable solution of given equation and belongs to hardy space ; with studying the growth of that solution by two ways ; through the maximum modulus and Brennan’s Conjecture and another by finding the supremum function of a volume of the surface area . Furthermore, we discussed the solution behaviour with meromorphic coefficients properties for given equation.