Question

Solve d²y/dx² + 16y = 0 differential equations.

Answer 1

Given (D² + 16) y =0 

The auxiliary equation is m² + 16 = 0 

⇒ m² = -16 

⇒ m = ± 4i 

It is of the form α ± iβ, α = 0, β = 4 

The complementary function (C.F) is e^0x [A cos 4x + B sin 4x] 

The general solution is y = [A cos 4x + B sin 4x]