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Rename integration variable in symbolic result

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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 Comments
Mohamed Gharbi
Mohamed Gharbi on 19 Sep 2022
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.

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Accepted Answer

Paul
Paul on 24 Feb 2023
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)

More Answers (1)

Surya
Surya on 23 Feb 2023
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 Comments
Surya
Surya on 24 Feb 2023
Edited: Surya on 27 Feb 2023
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 on 24 Feb 2023
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 ?

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