General desolve and conditions questions

[Han]

diff() takes 2 arguments, but lets you get away with specifying only 1. Usually, you would use diff() as: diff(function, var). If you leave out var, it is presumed to be x, so that diff(y) is really diff(y,x). The same applies for diff(x) -- which is interpreted as diff(x,x). That is, the function is "x" and the var is "x", so the derivative is just 1. So in your second case, you are asking desolve() to solve system of equations \( 1+ x = 5 \) and \( x=3 \); there is no solution to such a system.

I am not sure about #3.