$\phi(u, v) = (2u-v, 3u+2v) =: (x, y)$, compute: $ \phi^*(−ydx + 2xdy)$

Question

Let $ \phi : R^2 → R^2$ be the differentiable application defined by $\phi(u, v) = (2u-v, 3u+2v) =: (x, y) $. Compute:

$$\phi^*(−ydx + 2xdy). $$

What I thought:

\begin{align} (\phi^*w)(x)&=(\phi^*(−ydx + 2xdy))(x)\\ &=(\phi^*(−(3u+2v)d(2u-v) + 2(2u-v)d(3u+2v)))(x)\\ &=−(3u+2v)d(2u-v) + 2(2u-v)d(3u+2v) \end{align}

I don't know if it can be right and I wouldn't know how to proceed...