Find a Liapunov function to show asymptotically stable

Question

Consider the system: \begin{cases} \dfrac{dx}{dt} = y \\[12pt] \dfrac{dy}{dt} = -(1+x^{2})\,y-\sin(x) \end{cases} $(0,0)$ is a critical point of this system and I need to show that it is asymptotically stable by choosing a Liapunov function in form of $$V(x,y)=ax^2+2bxy+y^2$$ i.e. I need to choose $a$ and $b$ such that on some neighborhood of $(0,0)$ $D$, $V>0$ and $\dot{V}<0$. Where $\dot{V} =(2ax+2by)\,y+(2bx+2y)[-(1+x^{2})\,y-\sin(x)]$
I have no idea how to find such constant since for $x\in[-\pi,\pi]$, $\sin(x)>0$ when $x>0$ and $\sin(x)<0$ when $x<0$.