The authors consider the nonhomogeneous linear differential equation \(f^{(k)}+ A_{k-1}f^{(k-1)}+\cdots +A_0f=F\). Here, they use Nevanlinna's value distribution theory to investigate the complex oscillation of this system when the coefficients and the nonhomogeneous function \(F\) are transcendental entire functions of finite order, such that there exists an \(A_d\), \(0\leq d\leq k-1\) being dominant in the sense that either it has larger order than any other coefficient, or it is the only transcendental function. The main results are: for \(k\geq 2\), and the coefficients satisfy some given extra conditions, then all solutions to the differential equation are entire and satisfy \(\overline \lambda(f)=\lambda (f)=\sigma (f)=\infty\).