Question: Solving differential equations

If I have an ODE say dg/dx = g I can't seem to get a solution I can work with directly. Of course with dsolve I can get an expression which I can cut and paste into a function definition: ie.

ode:=diff(g(x),x) - g = 0

dsolve(ode)

g:=x->"output from dsolve"

 

But how do I get g(x) without the cut and paste. I have tried a number of ideas (rhs, subs) but I cannot get a function I can use  for example to calculate g(0) or g(1)

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