Rename integration variable in symbolic result

7 次查看（过去 30 天）
Mohamed Gharbi
Mohamed Gharbi 2022-9-18
编辑： Surya 2023-2-27
Hi,
There is an ambiguity in the name of vaiable x.
In the code below, I use x is a function of the variable t and Matlab uses it as the variable of integration.
How to change the name of the variable of integration ?
syms t m b y(t) y0 C x(t) % definitions of symbolic variables
cond = y(0) == C % inital condition
ode = m*diff(y,t) + b*y(t) == x(t) % definition of differential equation
ySymbSol(t) = dsolve(ode, cond) % Solution of the differential equation which uses x as integration variable !
The same result is obtained with Matlab 2022a and 2022b.
  3 个评论
显示 1更早的评论
Mohamed Gharbi
Mohamed Gharbi 2022-9-19
Yes. but in the book I'm writing, I use as notation for linear systems x(t) for input and y(t) for output. I would like, if possible, to keep these notations.

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Paul
Paul 2023-2-24
Ran in:
I don't know if I'd call this 'easily', but it gets the desired result (I believe).
syms t m b y(t) y0 C x(t) % definitions of symbolic variables
cond = y(0) == C; % inital condition
ode = m*diff(y,t) + b*y(t) == x(t); % definition of differential equation
syms u(t)
ySymbSol(t) = dsolve(subs(ode,x(t),u(t)), cond) % Solution of the differential equation which uses x as integration variable !
ySymbSol(t) = 
syms syms x tau
ySymbSol(t) = changeIntegrationVariable(ySymbSol(t),x,tau)
ySymbSol(t) = 
syms u
ySymbSol(t) = subs(ySymbSol(t),u,x)
ySymbSol(t) = 
syms x(t)

更多回答（1 个）

Surya
Surya 2023-2-23
Hi,
To avoid the ambiguity in the variable name, you can use a different variable for integration in the dsolve command. You can do this by providing the integration variable as the second argument to the dsolve function. Here's an example:
syms t m b y(t) y0 C x(t) tau
cond = y(0) == C; % initial condition
ode = m*diff(y,t) + b*y(t) == x(t); % definition of differential equation
ySymbSol(tau) = dsolve(ode, cond, tau); % solve the ODE with respect to tau
In this example, the dsolve function is called with the third argument set to tau, which specifies that tau is the independent variable in the differential equation. The second argument t is used as the integration variable in the solution. The resulting ySymbSol function will depend on tau instead of t.
  3 个评论
显示 1更早的评论
Surya
Surya 2023-2-24
编辑：Surya 2023-2-27
Here x(t) is renamed as g(t)
syms t m b y(t) y0 C g(t) % definitions of symbolic variables
cond = y(0) == C % inital condition
ode = m*diff(y) + b*y(t) == g(t) % definition of differential equation
ySymbSol(t) = dsolve(ode, cond)
And here is the final function
Now x becomes the variable of integration and g(x) is the function of x taking values from [ 0, t ].
Hope it helps.
Torsten
Torsten 2023-2-24
@Surya
See my discussion with the OP after the original question:
My comment was:
Should be easier to rename your function x, shouldn't it ?
And his answer was:
Yes. but in the book I'm writing, I use as notation for linear systems x(t) for input and y(t) for output. I would like, if possible, to keep these notations.
And my comment was:
I doubt you can specify it easily.
Or is it possible to specify it easily ?

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Symbolic Math Toolbox 的更多信息

标签

产品


版本

R2022a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by