Question: Solving a differential equation (involving phase space variables) and expanding to get an answer an explicit integral

Hi, I am looking for some help for a computation on Maple. I have the following objects

where lambda is a parameter, with pi and phi are functions of phase space (functions of x), m is just a constant (mass) and i is just the imaginary number.
I would then like to substitute these into

and solve for v=v(x). Finally, I wish to expand v(x) in increasing powers of 1/lambda. So it is of the form
 
And I would like to read off these 'coefficients' v_i. So I need a code that allows me to to pick an index and find out what the coefficients expressioni s. The answer (for odd indices I believe) will be an integral in terms of phase space variables. Here is an example which I believe (should) be right, perhaps up to some constants.
 

 Many thanks.
edit: I believe thelast expression was cut off early.  The image is here http://latex.codecogs.com/gif.latex?v_{-3}=\int_{-\infty}^{+\infty}%20dx%20\left[\left(\pi(x)-\partial_x%20\phi(x)\right)\sin(\phi)-\frac{1}{2m}\left(\partial_x%20\pi(x)-\partial_x^2%20\phi(x)\right)(\left(\pi(x)-\partial_x\phi(x)\right)^2%20-2m^2\cos(\phi))\right]