y''-4y'+8y=0

y'' - 4y' + 8y=0

Step1:

r² - 4r + 8 = 0

Step2:

r = ( -(-4)±√(-4)²- 4x1x8 ) / (2x1)

r = ( -(-4)±√-16 ) / (2x1)

r = 2 ± 2i

Step 3:

y = e^ax(c₁ cos(bx) + c₂ sin(bx))

Substitute a = 1, b = 2

y = e^2x(c₁ cos(2x) + c₂ sin(2x))