Description: The article is reviewed the inhomogeneous parabolic differential equation. It is belonged to Hill's class of equations with a quadratic potential member. The potential is approximated by a piecewise constant function. Than the equation is represented as equivalent system of equations. For this system of equations is got the analytical solution. The function fN(t,x) is found for t = tN = T. Evolution of function on the axis х = 0 is reviewed. The approximate analytical expression is got for the function f (t,x) for the starting condition f(t = 0, x) = 1.
Keywords: parabolic differential equation, potential, Hill's class of equations, coherence function, starting conditions, Riccati's equation, approximation