Taking Laplace transform of both sides:

Applying the initial condition ans simplifying gives:

Solving for Y:

For the first term, we use: , with a = 1 and n = 2.

So

For the second term, we express in partial fractions:

Comparing coefficients:

gives A = -2.

gives B = -1.

So

And

Putting our inverse Lapalce transform expressions together, the solution for y is: