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,