Nine kinds of general solutions of certain popular first-order ordinary differential equation are obtained by direct calculations. Compared with complete discrimination system for polynomials, our classifications of solutions straightly depend on the coefficients of the ordinary differential equation and hence are easier to be employed. According to the nine kinds of solutions, we establish thirty traveling wave solutions to the coupled systems of ion sound and Langmuir waves, including rational function solution, exponential function solution, trigonometric function solutions, hyperbolic function solutions and Jacobi elliptic function solutions. To the best of our knowledge, many of them are new. Solutions discussed in two recent articles are showed to be equivalent to some special cases of our thirty traveling wave solutions. Our solutions include the kink and anti-kink soliton solutions, dark and bright soliton solutions as well as periodic soliton solutions and solitary wave solutions. We believe that these solutions will be of great use to researchers concerning with nonlinear physical phenomena. In addition, the famous (1+1)-dimensional dispersive long wave equations is taken to illustrate the applicability of these thirty solutions.

通过直接计算得到了某些流行的一阶常微分方程的9种一般解。与多项式的完全判别系统相比，我们的解决方案分类直接取决于常微分方程的系数，因此更易于采用。根据这九种解，我们建立了离子声波与朗缪尔波耦合系统的三十个行波解，包括有理函数解，指数函数解，三角函数解，双曲函数解和Jacobi椭圆函数解。据我们所知，其中许多是新的。最近两篇文章中讨论的解决方案被证明与我们的三十种行波解决方案的某些特例等效。我们的解决方案包括扭结和反扭结孤子解决方案，明暗孤子解决方案以及周期性孤子解决方案和孤波解决方案。我们认为，这些解决方案对于涉及非线性物理现象的研究人员将非常有用。此外，还采用了著名的（1 + 1）维色散长波方程来说明这30个解的适用性。