Question

Solve d²y/dx² - 6(dy/dx) + 8y = 0 differential equations.

Answer 1

Given (D – 6D + 8) y = 0, D = d/dx

The auxiliary equations is 

m² – 6m + 8 = 0 

(m – 4)(m – 2) = 0 

m = 4, 2 

Roots are real and different 

The complementary function (C.F) is (Ae^4x + Be^2x ) 

The general solution is y = Ae^4x + Be^2x