On transcendental meromorphic solutions of certain type of nonlinear algebraic differential equations

The main purpose of this paper is to give the forms of transcendental meromorphic solutions of nonlinear differential equation of the form $$f^{n}f'+R(z)=p_{1}(z)e^{\alpha_{1}(z)}+p_{2}(z)e^{\alpha_{2}(z)}, $$ where \(R(z)\) is a rational function, \(p_{1}\), \(p_{2}\) are nonzero rational functions and \(\alpha_{1}\), \(\alpha_{2}\) are nonconstant polynomials. More precisely, we have shown the conditions concerning \(\frac{\alpha_{1}'}{\alpha_{2}'}\) that will ensure the existence of the possible meromorphic solutions of the above equation.