Solve the initial-value problem.

Question

y'' - 2y' + y = 0 , y(2) = 0 , y'(2) = 1

Answer 1

y = e^x (c1 + c2*x)
y' = e^x (c1 + c2 + c2*x)

Now plug in the initial conditions to get

e^2 (c1 + 2c2) = 0
e^2 (c1 + c2 + 2c2) = 1
Now just solve for c1 and c2