Hi,

i meet a partial differential equation seems not complicated

with(PDEtools):

PDE := (diff(f(x__1, x__2, p__1, p__2), x__1))*p__1/m-(diff(f(x__1, x__2, p__1, p__2), p__1))*(2*k*x__1-k*x__2)+(diff(f(x__1, x__2, p__1, p__2), x__2))*p__2/m-(diff(f(x__1, x__2, p__1, p__2), p__2))*(-k*x__1+2*k*x__2);

when i use

pdsolve(PDE);

i get nothing,but i sure

f=c*(p__1^2/m+p__2^2/m+4*p__1*p__2/m+6*k*x__1*x__2)

is the one solution of the differential equation .

how i can get solutions about of the above equation.

thanks .