CAS laplace transform w/ undefined function
09-13-2018, 04:35 AM
Post: #1
 wsprague Junior Member Posts: 9 Joined: Aug 2018
CAS laplace transform w/ undefined function
Hi all,

Working through my circuit book (Thomas & Rosa 2001), we are taking laplace transforms of undefined functions. For example:

L(dv(t)/dt + 6v(t)) = sV(s) + v(0) +6V(s)

How would I do this HP Prime / xcas? I would be happy with a link if there is one, but I have searched the docs as best I could.

As you can probably guess, we then solve for V(s) = .... and take the inverse transform, but that isn't the part where I am stuck currently. ( And forgive me if I got the above transform wrong, I am sure it is close and conveys the idea...)

Thanks!
09-13-2018, 05:47 AM
Post: #2
 parisse Senior Member Posts: 969 Joined: Dec 2013
RE: CAS laplace transform w/ undefined function
There is nothing builtin to handle unassigned function. If you want to check integration by part, you can run ibpu(exp(-s*x)*diff(f(x),x),exp(-s*x))
09-14-2018, 04:48 AM
Post: #3
 wsprague Junior Member Posts: 9 Joined: Aug 2018
RE: CAS laplace transform w/ undefined function
Do you or anyone have advice on how to use the laplace() transform function to solve a differential like the following?

dv(t)/dt + 6v(t) = sin(t)

In the book you take laplace transforms of each side, solve for V(s), but I don't see how to do that in xcas.

(Not sure why you suggested integration by parts, but it is highly likely I missed something.)

Thanks!
09-14-2018, 06:55 AM (This post was last modified: 09-14-2018 06:56 AM by parisse.)
Post: #4
 parisse Senior Member Posts: 969 Joined: Dec 2013
RE: CAS laplace transform w/ undefined function
Replace v(0) by it's value, solve for V(s)
y:=laplace(sin(t),t,s);
[vsol]:=solve(s*vs + v0 +6vs=y,vs);
ilaplace(vsol,s,t);

Check with desolve:
desolve([v' + 6v = sin(t) ,v(0)=v0],t,v)
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