Separation of Variables Error Analysis

The steps below show a student’s attempt to solve the differential equation $\displaystyle \frac{dy}{dx} = 2xy$ with the initial condition $y=3$ when $x=0$. In which step does an error first appear?

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

Step 2: $\ln |y| = x^2 + C$

Step 3: $\ln |y| = x^2 + \ln(3)$

Step 4: $\ln |y| - \ln(3) = x^2$

Step 5: $\ln \left|\frac{y}{3}\right| = x^2$

Step 6: $\frac{y}{3} = x^2$

Step 7: $y = 3x^2$