R语言可以找到一阶微分方程的通用解吗？ [英] Can R language find a generic solution of the first order differential equation?

问题描述

R语言能否找到一阶微分方程的通用解？

Can R language find a generic solution of the first order differential equation?

例如：

(5x-6)^2 y' = 5(5x-6) y - 2 

PS：

可以很容易地手动解决，即特定的解决方案是：

PS:
That can be easily solved by hand, i.e. particular solution is:

y = 1/(5(5x-6))

和通用

C*(5x-6)

我需要了解R是否可以做到？

I need to understand whether R can do it?

推荐答案

我们可以使用R库 deSolve 来获得ODE。有关详细信息，请参见？deSolve 。

We can use the R library deSolve to obtain numerical solutions of ODEs. See ?deSolve for details.

以下是基于ODE的精通示例。

Here is a worked-through example based on your ODE.

1. 加载R库

1. Load the R library

library(deSolve);

定义微分方程

Define the differential equation

# Define the function
f <- function(x, y, params) list((5 * (5 * x - 6) * y - 2) / (5 * x - 6)^2)

设置 x 待求解的值和初始条件

Set x values for which to solve and initial condition

# x values for which to solve
x <- seq(2, 10, length.out = 100);

# Initial value y(x=2) = 1/20
y0 <- 1/20

解决ODE问题

Solve the ODE

# Solve ODE
df <- as.data.frame(ode(y0, x, f, parms = NULL));

从 deSolve <绘制理论（代数）解和数值解/ code>

Plot theoretical (algebraic) solution and numerical solution from deSolve

# Plot
library(ggplot2);
ggplot(df, aes(time, `1`)) +
    stat_function(
        fun = function(x) 1/(5 * (5 * x - 6)),
        aes(colour = "Theoretical"),
        size = 4) +
    geom_line(aes(colour = "deSolve"), size = 2) +
    labs(x = "x", y = "y")

< a href = https://i.stack.imgur.com/E2qlr.png rel = noreferrer>

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