n.颂诗,颂歌
ode的复数

原形：ode复数：odes

The differential equation y'' + 4y = 0 describes simple harmonic motion.
这个微分方程y'' + 4y = 0描述了简谐运动。
An ordinary differential equation (ODE) is a mathematical equation containing one or more functions of one independent variable and its derivatives.
常微分方程（ODE）是一个数学方程，包含一个或多个独立变量及其导数的函数。
Solving a second-order ODE involves finding the function y(x) that satisfies the given equation.
解一个二阶常微分方程意味着找到满足给定方程的函数y(x)。
A linear ODE, like dy/dx + 2y = 5, can be solved using standard methods.
线性常微分方程，如dy/dx + 2y = 5，可以使用标准方法求解。
Non-linear ODEs often require numerical methods to find approximate solutions.
非线性常微分方程通常需要数值方法来找到近似解。
The Lotka-Volterra equations are a set of coupled ODEs modeling predator-prey dynamics.
洛特卡-沃尔伯格方程是一组耦合的常微分方程，用于模拟捕食者-猎物动态。
Stability analysis of ODEs helps predict the behavior of systems over time.
常微分方程的稳定性分析有助于预测系统随时间的行为。
Many physics problems, such as wave equations, can be formulated as partial differential equations, but they can also be reduced to ODEs in certain cases.
许多物理问题，如波动方程，可以用偏微分方程表示，但在某些情况下也可以转化为常微分方程。
The Euler method is a basic numerical technique for solving first-order ODEs.
欧拉方法是一种基本的数值技术，用于解决一阶常微分方程。
Boundary value problems, where initial conditions are not enough to determine a unique solution, often involve solving systems of ODEs.
边界值问题，初始条件不足以唯一确定解的情况，通常涉及解决一组常微分方程。