Consider the following initial value problem:
[
y^{prime prime}+16 y=left{egin{array}{ll}
2 t, & 0 leq t<3 \
0, & t geq 3
end{array} quad y(0)=0, y^{prime}(0)=0
ight.
]
Using ( Y ) for the Laplace transform of ( y(t) ), i.e., ( Y=mathcal{L}{y(t)} ), find the equation you get by taking the Laplace transform of the differential equation and solve for
[
Y(s)=
]