The second Painleve equation
is investigated on the basis of the asymptotic analysis of a boundary value problem for singularly perturbed nonlinear ordinary differential equations describing the operation of an electrostatic probe in a collisional plasma. The behavior of certain properties of the equation and its regular solutions with the asymptotics
is considered within the framework of electrostatic-probe theory. Conditions satisfied by these solutions at a certain point
are indicated, which makes it possible to calculate the solutions numerically.