I am trying to solve the following differential equation using Laplace and am not sure where I am going wrong: $$\frac{\text{d}^2x}{\text{d}t^2} + 2\frac{\text{d}x}{\text{d}t} + 5x=0,$$ where $x(0)=1$ and $\dot x(0)=0$. $$\mathbf{L}\left[\frac{\text{d}^2x}{\text{d}t^2} + 2\frac{\text{d}x}{\text{d}t} + 5x=0\right]=\mathbf{L}[0]$$
Then $$s^2X(s) - sx(0) - \dot x(0) + 2(sX(s)-x(0)) + 5X(s)= 0$$
Then $$X(s)= \dfrac{2+s}{s^2+2s+5}$$
What do I do next please and is this even correct? I don’t think it is as the denominator can’t be factorised?