R中是否有符号ODE求解器？ （ODE =常微分方程） [英] Is there symbolic ODE solver in R ? (ODE = ordinary differential equation)
问题描述
问题：R中是否存在符号ODE求解器？ （ODE = 常微分方程）
Question: Is there symbolic ODE solver in R ? (ODE = ordinary differential equation)
恐怕没有...但是让我向专家确认...
I am afraid there is NO... but let me confirm from experts ...
例如，解决：
> (5x-6)^2 y' = 5(5x-6) y - 2
这里： y-未知函数，y'-其导数
Here: y - unknown function, y' - its derivative
（易于解决：y = 1 /（5（5x-6））+ C *（ 5x-6），但我想从R中得到答案。
(It is easy to solve by hands: y = 1/(5(5x-6)) + C* (5x-6) , but I want to get that answer from R).
我所知道的：
1）有数字（非符号）求解器：
我知道有数字ODE求解器，例如library（deSolve），
参见此处的答案：
R语言能否找到一阶微分方程的通用解？
I know there are numerical ODE solvers like library(deSolve), see answer here: Can R language find a generic solution of the first order differential equation?
2）有符号包：（但它们似乎不包含ODE求解器）
2) There are symbolic packages : (but they do not seem to contain ODE solvers)
R中有符号包，例如
，请参见Ryacas和rSymPy，以及b中的一些基本符号计算ase R，请参阅：
https://stats.stackexchange.com/questions / 4775 / symbolic-computation-in-r / 4778
There are symbolic packages in R like see Ryacas and rSymPy and also some basic symbolic calculation in base R, see: https://stats.stackexchange.com/questions/4775/symbolic-computation-in-r/4778
3）R的各种微分方程求解器的简要概述：
https://cran.r-project.org/web/ views / DifferentialEquations.html
但是我找不到sumbolic ODE求解器（（（（
However I was unable to find sumbolic ODE solvers (((
推荐答案
我曾经玩过 Ryacas ，实际上，您可以得到一些简单ODE的符号解决方案，而无需太多的工作。不幸的是，YACAS无法为您的示例ODE找到解决方案。但是，根据您正在探索的ODE，这可能仍然有用。如果没有，那么我很乐意删除该帖子。
I've had a play around with Ryacas, and you can in fact get symbolic solutions to some simple ODEs without too much work. Unfortunately, YACAS fails to find a solution for your example ODE. However, depending on the ODEs you are exploring, this might still be of use. If not, I'm happy to remove this post.
作为一个简单的初始示例，让我们考虑以下ODE： y ''+ y = 0 ：
As an initial simple example, let's consider the following ODE: y'' + y = 0:
-
加载库
Load the library
library(Ryacas);
因为 Ryacas 只是一个与YACAS的接口，我们可以使用YACAS' OdeSolve 来解决ODE
Since Ryacas is just an interface to YACAS, we can use YACAS' OdeSolve to solve the ODE
yacas("OdeSolve( y\'\' + y == 0 )")
#expression(C70 * exp(x * complex_cartesian(0, -1)) + C74 * exp(x *
# complex_cartesian(0, 1)))
这给出了正确的解决方案 const * exp（-ix）+ const * exp（+ ix）。
This gives the correct solution const * exp(- ix) + const * exp(+ ix).
不幸的是，在使用您的特定示例时， OdeSolve 找不到解决方案：
Unfortunately when using your particular example, OdeSolve fails to find a solution:
yacas("OdeSolve( y\'\' == (5 * (5 * x - 6) * y - 2) / (5 * x - 6)^2 )")
#expression(y(2) - (5 * ((5 * x - 6) * y(0)) - 2)/(5 * x - 6)^2)
当我们使用 YACAS在线演示时，也会发生同样的情况。 。
The same happens when we use the YACAS online demo.
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