Unfortanely could not follow complete the handling of the partial deratives and integrating
In general integrating in 1,2 and 3 variables and their constants?
What says that one partial derative is zero in u=f(x,y,z) ?
Could this figure out in Maple symbolically ?..yes it can, but how
With pdsolve( two or more variables) and dsolve (one variable)
A := exp(x)*cos(y) + y*z
f := int(A, x) + g(y, z);
f := y z x + exp(x) cos(y) + g(y, z)
The constant is here g(y,z)
Now diff(f,y) should be B. Obtain that derivative and compare to B.
diff(y*z*x + exp(x)*cos(y) + g(y, z), y) - B = 0;
--- g(y, z) = 0
This says g(y,z) is independent of y, so g(y,z) = h(z), a function of z only. That makes f become
ff := eval(f, g(y, z) = h(z));
ff := y z x + exp(x) cos(y) + h(z)