Answer:

Step-by-step explanation:
A second order linear , homogeneous ordinary differential equation has form
.
Given: 
Let
be it's solution.
We get,

Since
, 
{ we know that for equation
, roots are of form
}
We get,

For two complex roots
, the general solution is of form 
i.e 
Applying conditions y(0)=1 on
, 
So, equation becomes 
On differentiating with respect to t, we get

Applying condition: y'(0)=0, we get 
Therefore,
