Inhomogeneous Burgers Equation and the Feynman-Kac Path Integral
  By linearizing the inhomogeneous Burgers equation through the Hopf-Cole transformation, we formulate the solution of the initial value problem of the corresponding linear heat type equation using the Feynman-Kac path integral formalism. For illustration, we present the exact solution for the forcing term of the form: $F(x,t)=\omega ^2x+f(t).$ We also present the initial value problem solution for the case with a constant forcing term to compare with the known result. 
Hans J. Wospakrik and Freddy P. Zen