How to apply initial conditions in second-order differential equations

The solution to the second-order differential equation has been obtained as follows.



If we want to find the solution by applying the initial conditions y(t)=0, y'(t)=0,

what should I do in the following steps?

thank you for your help.

Once you've got y(t) you could simply do the following:

If you don't need the function v(t), you can specify the initial conditions directly: (example 10.2 in https://github.com/sn-code-inside/Technische-Mechanik-mit-SMath)