I want to solve the following vector-differential equation for $\phi$ in terms of the rest of the variables.
$\phi = -\tau \mathbf{v}\cdot \mathbf{F}+(\mathbf{v}\times\mathbf{s})\cdot\nabla_{\mathbf{v}}\phi$.
I am new to vector calculus, so I am not sure how to proceed. I tried taking $\nabla_{\mathbf{v}}$ on both sides of the equation but couldn't proceed.