Solving Laplace Transformations with 4 initial conditions

Question

The problem start with the 4th derivative of y (y\'\'\'\')=f(x), and f(t)=3H(t-2/8)-3H(t-4/8) , H being heaviside. There\'s initial conditions y(0)=0, y\'(0)=0, y(1)=0, and