Equation is x"-4x=0, general solution is x(t) = c1e^-2t+c2e^2t, initial condition is x(0) = 1, x'(0)=0

Step-by-step explanation:

The given differential equation is

The characteristics equation is given by

Therefore, the solution of the DE is given by

On differentiating, we get

Apply the initial conditions

x(0)=1

Second condition is x'(0)=0

Add (i) and (ii)

Substituting this value in (ii)

Hence, the solution of the DE is

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a