Final answer:
To solve the differential equation y''-2y'+2y=0, assume a solution of the form y = ce^(ax)sin(bx + c), solve the quadratic equation to find the values of a and b, and express the final solution in the given form.
Step-by-step explanation:
To solve the differential equation y''-2y'+2y=0, we can assume a solution in the form of y = ce^(ax)sin(bx + c). Plugging this solution into the equation gives us a quadratic equation in terms of a and b. To find the values of a and b, we can solve this quadratic equation. The solutions will give us the values of a and b, which we can then use to write the final solution in the form ce^(ax)sin(bx + c).