Error in Solving a Separable Differential Equation

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