Find surface in $\mathbb{R}^3$ with certain tangent spaces By Frobenius Theorem, in $\mathbb{R}^3$ there exists a smooth surface
whose tangent space is spanned by the vector fields $V(x,y,z)=(x^2+y^2,0,-y)$
and $W(x,y,z)=(0,x^2+y^2,x)$. 
How can I find this surface?
Is there in general a way to find it when the vector fields are algebraic?

Note that $\omega=y\,dx - x\,dy+(x^2+y^2)\,dz$ annihilates both $V$ and $W$. Also note that if we set $f(x,y,z)=1/(x^2+y^2)$, then $d(f\omega) = 0$, so $f\omega$ is locally exact. Indeed, the integral manifolds are the graphs $z=\theta+c$ of the multivalued function $\theta(x,y)$ (defined away from $x=y=0$).
