DE 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 = 2, b = 2

y = e^2x(c₁ cos(2x) + c₂ sin(2x))