Solving for C in a function

Questions
1

Been looking everywhere on how to solve for C in the given function. y(x)=Tan(X^3+C), y(0)=1. Below is my code or at least what I could come up with in the last few days. Any help would be much appreciated. Don’t really need the answer but a push in the right direction.

Clear[y, x]
x0 = 0
y0 = 1
eqn1[x_, C_] = Tan[x^3 + C]
cSoln = Solve[eqn1[x0, C] == y0, C]
2

y[x_]:=Tan[x^3+c];
Reduce[y[0]==1,c]

3

C[1] [Element] Integers && C == [Pi]/4 + [Pi] C[1]

Is this Mathematica’s way of saying C = Pi/4 ? Thanks for the reply!

4

its Mathematica’s way of saying c = pi/4 + n pi

5

Thanks!

6

By the way, note that C is a Protected System symbol in Mathematica. It is a good practice not to use symbols beginning in an upper case letter or your symbols. Also, if when you first type a symbol it is colored black rather than blue, then it is something that is already defined in some way.

?C

C[i] is the default form for the ith parameter or constant generated in representing the results of various symbolic computations.