Answer:

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,
