帮忙翻译一段（数学研究类的）,拒绝机译!（有大加分!）

帮忙翻译一段（数学研究类的）,拒绝机译!（有大加分!）
We demonstrate the applications of ODE in both deterministic and stochastic systems. As an application in deterministic systems, we apply ODE to solve a simple gross domestic product (GDP) model and an investment model of a firm. Gould (1968) studies the adjustment costs in the theory of investment of a firm by considering a rationally managed firm in a competitive industry, acting to maximize the present value of all future net cash flow. To this end, Gould (1968) derives an Euler-Lagrange equation, which leads to a second order differential equation. By the classical solution technique and the Laplace transform, we obtain the optimal capital input function. As an application in stochastic systems, we employ ODE in a jump-diffusion model and derive the expected discounted penalty given the asset value follows a phase-type jump diffusion process. In particular, we study capital structure management model and derive the optimal default-triggering level. Chen et al. (2007) derive an integro-differential equation for the expected present value of a firm, and apply ODE approach to solve the equation.
The remainder of this chapter is organized as follows. In section 82.2, we introduce some fundamental concepts and two solution techniques. In particular, the classical solution technique is introduced in sub-section 82.2.1, the Laplace transform is introduced in sub-section 82.2.2 and the Euler-Lagrange equation is introduced in sub-section 82.2.3. The applications of ordinary differential equation are illustrated in sections 82.3 and 82.4. In particular, it application in a deterministic system is in section 82.3 by considering a simple GDP model and an investment model for a firm. Its application in a stochastic system is demonstrated in section 82.4 by considering a capital structure management model. Finally, this chapter is concluded in section 82.5.
注:ODE以及ordinary differential equation均为为常微分方程
翻译好的加80分！

我们论证了常微分方程在确定性系统和随机性系统中的应用.为了论证常微分方程在确定性系统中的应用,我们将其应用于一个简单的国内生产总值模式和一个公司的投资模式.Gould (1968)研究了在一个公司得到合理管理并且处于激烈竞争中的前提下,其理算费用是否会使其未来净现金流量现值达到最大.为此,Gould (1968)运用了欧拉-拉格朗日方程,该方程演化出了一个二阶微分方程.通过运用经典解法和拉普拉斯变换,我们得出了最佳资本投入函数.为了论证常微分方程在随机性系统中的应用,我们将其应用于一个跳跃扩散模式,得出了给定资产值随相形跳跃扩散的变化过程中的预期罚金折现值.我们还特别研究了资产结构管理模式,并得出了最佳违约触发点.Chen et al.(2007) 得出了一个公司预期现值的积分微分方程,并使用常微分方程的方法解答了此方程.
本章剩余部分的组织结构如下：在82.2节中,我们介绍了一些基本概念和两种解决方法.82.2.1小节中特别介绍了经典解法.82.2.2小节中介绍了拉普拉斯变换.82.2.3小节介绍了欧拉-拉格朗日方程.82.3和82.4节中举例说明了常微分方程的应用.82.3节中举例说明了常微分方程在以下确定性系统中的应用：简单的国内生产总值模式和公司的投资模式.82.4节中举例说明将常微分方程应用于一个资本结构管理模式的随机性系统.最后,82.5节对本章进行了总结.
我的译文是基于原文的,有些术语可能不是非常准确,你看的时候多从专业的角度看吧.采纳就加分呀!
我还找到了这篇论文PDF格式的英文版：
http://andromeda.rutgers.edu/~jshi/Chapter%2082%20-%20Application%20of%20ODE%20in%20FER-April%202009.pdf