Question $5$: Solve the following by Laplace transforms and Inverse laplace

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

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

$(c)\frac{d^{2}x}{d{t}^2}+3\frac{dx}{dt}+x=1,x(0)=x^{\text{'}}(0)=0$

$\frac{d^{2}y}{d{t}^2}-2=0,$ with $y^{\text{'}}(0)-y(0)-0$

d$.$