Question

Solve the initial value problem d²x/dt² + 5dx/dt + 6x = 0,  given that x(0) = 0, dx/dt(0) = 15.

Answer 1

We have (D² + 5D + 6) y = 0

A.E.. m² + 5m + 6 = 0

(m + 2) (m + 3) = 0

⇒ m = – 2, – 3

Therefore general solution is

x = x (t) = C₁e^–2t + C₂e^–3t ...(1)

This is the general solution of the given equation

Now, consider, x (0) = 0

Eqn. (1), becomes x (0) = C₁(1) + C₂(1)

i.e., C₁ + C₂ = 0 ...(2)

Also we have from Eqn. (1),