Final answer:
To find the solution y for the differential equation y'' - 4y' + 4y = 0 with specific initial conditions, we can use the technique of assuming a general solution and solving the characteristic equation.
Step-by-step explanation:
To find the solution y for the differential equation y'' - 4y' + 4y = 0, with initial conditions y(0) = 0 and y'(0) = -3, we can assume a general solution of the form y = e^(rt), where r is a constant. By substituting this into the differential equation, we get the characteristic equation r^2 - 4r + 4 = 0. Solving this quadratic equation gives us the roots r = 2, 2. Therefore, the general solution is y = C1e^(2t) + C2te^(2t), where C1 and C2 are constants determined by the initial conditions.