Implicit Differentiation?

Question

Find y = f(x) by solving the differential equation dy/dx =2xy with the initial condition f(0) = 2

Answer 1

We rewrite this as as dy/y = 2x, which yields a solution ln(y) = x² + c, or y = Ce^x2 (note that C = e^c)

As f(0) = 2, C = 2

Thus, the solution is f(x) = 2 e^x²