What are the rules for integrating a PDE of say 2 or more variables? And where can i learn more about these ? For example, i am asked to find the solution by direct integration of
Now ; And
Have i done this correctly ? I can't seem to find much information on integrating PDEs online. I am unsure of the arbitrary f(x),g(y) and h(z) functions, and how i have worked with them? Any help is much appreciated!
Well...i don't know...My knowledge of integrating a PDE is secondary, i have just picked things in physics, other than that i have somehow managed to skip an education in this field ! Am currently doing a third year applied math course and feel i might have skipped quite a necessary course on this area.Where could i find out more on the integration of partials? What might it look like if the variables were not seperable?
This is what I'd do: Assuming the mixed partials are equal and you want to integrate with respect to x, than y, then z, I'd write as:
(in general, you can't assume the arbitrary constant is separable so it's f(x,y))
Then integrating with respect to z:
Also, I'd recommend "Basic Partial Differential Equations" by Bleecker and Csordas.
I think you can drop that last single integral as it's still just an arbitrary function of z such as .