Unresolved symbolic integral - How to solve numerically?

I need to solve a complex 1st order PDE with 3 spatial inputs (x,y,z) and two angles (theta,phi). Only spatial partials are involved in the equation. I eliminated the spatial partials with the method of characteristics and now I am left with an ODE. The solution however involves indefinite integrals that the symbolic toolbox cannot solve (and I definitely cannot solve on my own).

Can I somehow use one of the 'integral' function to solve these indefinite integrals? My problem with that approach is that I don't know what limits of integration to provide to the function.

Alternatively I would consider the PDE toolbox to solve directly the PDE, but it does not solve 1st order PDEs to my knowledge.

[Torsten]

By applying boundary conditions to your PDE, your indefinite integrals should change to definite ones.

Best wishes

Torsten.

[Vasilis Andriopoulos]

I found out that a symbolic solution is not possible for this problem without unwanted simplifications. Thank you for your answer.

Answer 1

[John D'Errico]

No. You cannot use a numerical integration tool (integral) to solve indefinite integrals, and certainly not symbolic ones.

Not all problems have solutions. The art of mathematics is to find a way to solve intractable problems, instead of throwing them at a computer and hoping the computer can solve it for you. Computers are great at solving messy problems that are tractable, if only you had a vast amount of time and patience.

[Vasilis Andriopoulos]

Thank you.