For the following initial value problems, find the solution $x(t)$ using the Laplace transform.

$(1)\frac{d^{2}x(t)}{d{t}^2}+11\frac{dx(t)}{dt}+24x(t)=2,x(0)=0,x^{\text{'}}(0)=1$

$(2)\frac{d^{2}x(t)}{d{t}^2}+10\frac{dx(t)}{dt}+25x(t)=0,x(0)=1,x^{\text{'}}(0)=1$