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** 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.

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Keywords:
** parabolic differential equation, potential, Hill's class of equations, coherence function, starting conditions, Riccati's equation, approximation

Protsai, N.T. (2015), “Reshenie parabolicheskogo differentsialnogo uravneniia s peremennym potentsialom” [Solution parabolic differential equations with alternative potential],