# Rename integration variable in symbolic result

3 views (last 30 days)
Mohamed Gharbi on 18 Sep 2022
Edited: Surya on 27 Feb 2023
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.
Torsten on 19 Sep 2022
I doubt you can specify it easily.

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)
Torsten on 25 Feb 2023
We say: From behind through the chest into the eye :-)

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.
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 ?
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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