Solve the inital value problem by using Laplace transform
First noticed that the initial condition are not at t=0.We can applythe Laplace transform of derivative is to have the initial condition at t=0.
This mean that we will need to formulate the IVP in such a way thatthe initial condition are at t=0.
We need to change the variable
By using chain rule,
Hence,the initial condition for
Now,the equation (2) becomes
Apply the Laplace transform on both sides,then