Algebraic resolution of the Burgers equation with a forcing term

We introduce an inhomogeneous term, f ( t , x ), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions f ( t , x ) which depend nontrivially on both t and x , we find that there is just one symmetry. If f is a function of only x , there are three symmetries with the algebra s l (2, R ). When f is a function of only t , there are five symmetries with the algebra s l (2, R ) ⊕ s 2 A 1 . In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.