A student attempted to find the particular solution to the differential equation $$\displaystyle \frac{dy}{dx} = 4x^3 y^2$$ with the initial condition $$y(0) = 1$$. The student’s work is shown below. In which of the following steps does an error first appear?

Step 1: $$\displaystyle \int \frac{1}{y^2} dy = \int 4x^3 dx$$

Step 2: $$\displaystyle \frac{1}{y} = x^4 + C$$

Step 3: Using the initial condition: $$\displaystyle \frac{1}{1} = 0^4 + C$$, so $$C = 1$$

Step 4: $$\displaystyle \frac{1}{y} = x^4 + 1$$

Step 5: $$y = \frac{1}{x^4 + 1}$$