Notation with DSOLVE is unclear

I am solving this differential equation

syms y(x) 
dsolve(diff(y) == 4/100*y)

that gives

C4*exp(x/25)

What does the C4 means? I know there should be a constant representing the degree of freedom, but I noticed that if I change the coefficient in my equation the C. changes.

I am confused, it's just a way of indexing different constants, or is that a multiplier(the * is missing though)?

Answer 1

[Walter Roberson]

It is just a way of indexing different constants. Also, if you run the same equation through twice you will probably get out two different constants, which is done so that you do not accidentally tie the equations together. For example,

A = dsolve(eqn1);
B = dsolve(eqn1);
C = [A, B];

Then the two parts of C need to have different constants (after all, they might represent different initial conditions), so dsolve() will emit different C* symbols.