Use Laplace transform to solve the initial value problem \[ y^{\prime \prime}+9 y=g(t) ; \quad y(0)=1 ; \quad y^{\prime}(0)=0 \] where \[ g(t)=\left\{\begin{array}{ll} 6, & 0 \leq t<\pi \\ 0, & \pi \leq t<1 \end{array}\right. \]