(Solved): Use the Laplace transform method to solve the following differential equations for x(t) : dt2d2x ...

Use the Laplace transform method to solve the following differential equations for $x(t)$ : $\frac{d^{2}x}{d{t}^2}?2\frac{dx}{dt}+x=0$ subject to the initial conditions $x(0)=1,x^{?}(0)=0$. Use the Second Shift Theorem or otherwise to solve the following ordinary differential equation for $x(t)$ $\frac{d^{2}x}{d{t}^2}+4x=4H(t?1),$ subject to the initial conditions $x(0)=0,\frac{dx}{dt}(0)=1$ and where $H(t)$ is the Heaviside step function.