I need to solve this Partial Differential Equation for $\lambda(x,y)$,

$$\frac{\partial \lambda}{\partial x} + h(x,y)\frac{\partial \lambda}{\partial y} - \lambda \frac{\partial h}{\partial y} = 0$$ where $$\frac{dy}{dx} = h(x,y).$$

The additional information given is $\lambda$ is a bivariate polynomial in $x$ and $y$. My initial approach was to try using the method of characteristics, but I know I can't since $y$ is dependent on $x$.

So I guess I should use some sort of degree bound, and find the coefficients by equating powers on both sides, However I just wanted to know if there is actually a better method to do this before I proceed? And even if it has to be done by powers, how do I get the degree?

Additional information: And this PDE is part of a Symmetry Solver to find the infinitesimals, $\xi$ and $\eta$ of the transformed canonical co-ordinates of a first order differential equation.