Laplace Transform with Convolution - I'm really confused on how to solve this one. Thanks in advance!!

dy/dt = (t^3) * t

where ( * ) = convolution


for y(0) = 6

and

t ≥ 0


*****Thanks you for all of your help!! I really appreciate it!!!*****

Note that L{t^3 * t}
= L{t^3} · L{t}
= (3!/s^4) · (1/s^2)
= 6/s^6.

So, applying L to both sides of the DE yields
s Y(s) - y(0) = 6/s^6.
==> s Y(s) - 6 = 6/s^6.

Solve for Y(s):
Y(s) = 6/s + 6/s^7.

Inverting term yields
y(t) = 6 + (1/6!) t^6 = 6 + (1/720) t^6.

I hope this helps!