Hi, I am trying to solve for the steady state of Fokker Planck equation. The answer should be Boltzmann distribution but I am not getting it. Could someone please let me know where I messed up:
`U[x_] = 1/2 k x^2;`
`FPEss = 0 == D[(D[U[x], x])*p[x, t], x] + D[p[x, t], {x, 2}];`
`bc1 = p[-Infinity, t] == 0; bc2 = p[Infinity, t] == 0; ic =
p[0, t] == DiracDelta[x];`
`DSolve[{FPEss, bc1, bc2, ic}, p[x, t], {x, t}, Assumptions -> k > 0]`