How to solve these ODEs

[Asad]

I need to solve these ODEs using MathCAD Prime 2.0. Image of the ODEs is attached.

With initial and end boundary conditions:

vf (0)= 0.2

xf (0)= 0.011

Pf (0.34 @ end/exit) = 1.01*10^5

Tf (0) = 80

Thanks!

[Fred_Kohlhepp]

You have quite a few undefined terms (constants?)

These might be solvable numerically but all constants would need to be defined.   A symbolic solution is beyond Mathcad. 

And how many of the terms on the left hand side of your third equation are functions (or is that three constants times the derivative of temperature?)

[Asad]

Thank you for replying. I discussed it with a professor I know, and he proposed a solution which I will try. And yes you are correct I did not add the details of all the constants, my apologies but as for now I would close this question.

And also, the third equation is confusing about whether all the variables are inside the derivative. I would have to derive another one in its place.

[LucMeekes · Accepted solution]

As Fred wrote, you have a few things to clear up, before this can be solved. With Mathcad (Prime) your best way is to try a solve block.

One other observation:

If I interpret right (in Mathcad, as well as in mathematics, x is different from X), your first two equations only deal with x.f(z) and v.f(z) and their derivatives, and you have boundary conditions for x.f(0) and v.f(0). That should allow you to solve x.f(z) and v.f(z) independently of the rest.

The fourth equation gives you P.f(z) once v.f(z) is known.

That leaves the third equation...

I suggest you start entering the equations into Prime and reply back here in case you get stuck. Then be sure to attach the Prime sheet, not just a picture.

Success!
Luc

[Asad]

Thank you for replying. I discussed it with a professor I know, and he proposed a solution which I will try. And yes you are correct I did not add the details of all the constants, my apologies but as for now I would close this question.

And also, the third equation is confusing about whether all the variables are inside the derivative. I would have to derive another one in its place

[LucMeekes]

Thank you for this personal reply.

But it was not necessary, there's no need to copy responses in the same thread. Your reply to Fred is sufficient information.

If you want to close this discussion, please do so (close it), possibly by marking it answered.

If you ever want to discuss this topic again, you could make a refernce to this discussion, if that helps.

Success!

Luc