I'm guessing I have to solve for y in terms of x, let y = 1 and x = 1, then solve for C?

This is what I did:

\(\displaystyle y = e^\frac{x^3}{3} + C\)

Since \(\displaystyle y(1)=1\),

\(\displaystyle 1=e^\frac{1}{3} + C\)

\(\displaystyle C=1 - e^\frac{1}{3}\)

For some reason this doesn't feel right.

Then the original equation should be:

\(\displaystyle y = e^\frac{x^3}{3} + 1 - e^\frac{1}{3}\)