Let's start by separating the variables: dy = (4 / e^x) dx

Now, we can integrate both sides of the equation: ∫ dy = ∫ (4 / e^x) dx

Integrating, we get: y = ∫ (4 / e^x) dx

To integrate 4 / e^x, we can use the fact that the integral of e^x is e^x:

y = -4e^(-x) + C

Now, we can apply the initial condition y = 3 when x = 0 to determine the value of the constant C:

3 = -4e^(-0) + C

3 = -4(1) + C

3 = -4 + C

C = 7

Therefore, the particular solution of the given equation, satisfying the initial condition, is:

y = -4e^(-x) + 7.