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Solving for series of equations that include functions, derivatives, and boundary conditions

SOLVED

Re: Solving for series of equations that include functions, derivatives, and boundary conditions

What is the error message?
What does it say?

Re: Solving for series of equations that include functions, derivatives, and boundary conditions

Thanks for trying to solve it this way Fred! I input that data into my solve block and I get an error highlighting the 'x' in the Odesolve function that says that "The arguments of the Odesolve are not correctly specified"

Re: Solving for series of equations that include functions, derivatives, and boundary conditions

The error on the V(x) in the plot says "This variable is undefined. Check that the label is set correctly"

Re: Solving for series of equations that include functions, derivatives, and boundary conditions

Whoa that looked like magic to me - but you're saying this definitely won't work with mathcad prime?


@LucMeekes wrote:

Well OK, with Mathcad 11 (but just that version, nothing before, and nothing after) you can automate this completely for solving y(x):

LM_20181203_SolveDE3.png

For more information look here:

https://community.ptc.com/t5/PTC-Mathcad/A-Classical-Math-Problem-from-a-Classical-Text-Differential...

 

Luc


 

Re: Solving for series of equations that include functions, derivatives, and boundary conditions

Luc, If I understand correctly, this example uses MathCAD to help do the arithmetic steps in the hand calculations. This may be useful since my more complex example gets into the weeds with so many different variables flying around


@LucMeekes wrote:

"I can solve this problem by hand, symbolically, is there a way to formulate the problem in mathCAD so it can do the same?"

 

Mathcad has no provision to symbolically solve differential equations (DE). With simple DE some simple manipulation is possible that gives satisfactory results.

Starting with your initial formulation of the problem this is how you could go about:

LM_20181203_SolveDE1.pngWith that settled, we can go on:

LM_20181203_SolveDE2.png

Mathcad 11 file attached.

Success!
Luc


 

Re: Solving for series of equations that include functions, derivatives, and boundary conditions

This, in the way it is shown, will definitely NOT work with any version of Prime to date, nor with any version of Mathcad other than 11.

If you need to do a lot of this kind of stuff, symbolically, you can use the symbolics of Mathcad or Prime to help you solve Differential Equations via the Laplace domain (essentially that's what my sheet in Mathcad 11 does). But it involves work by you. If you want ready symbolic solutions to DE's out of the box, then you need to resort to other applications: Maple & Mathematica are two of the most powerful I know of, you may want to check out Maxima (it's free). (Why do all names of these applications start with "Ma"?)

It so happens that the symbolic machine in Mathcad 11 is Maple. As of Mathcad 14 they replaced that with MuPad. (Ah, that one's not part of the pack!)

But... If you can live with numeric solutions, Mathcad will be your friend, and if you then need to include units as well, then Prime may be your better friend.

 

Success!
Luc

Re: Solving for series of equations that include functions, derivatives, and boundary conditions

And.... did you check the label?

Are the labels of the V as a result of Odesolve and the V in your plot labelled the same?

Re: Solving for series of equations that include functions, derivatives, and boundary conditions

Luc, thanks again for all the help you are giving.

The V is indeed a V.

Highlighted

Re: Solving for series of equations that include functions, derivatives, and boundary conditions

So does it show a graph now?