At any given temporal coordinate, the rate of change at which the vertical position of an object moving in a two-dimensional (2-D) plane varies with respect to its horizontal position is governed by...

Extracted text: At any given temporal coordinate, the rate of change at which the vertical position of an object moving in a two-dimensional (2-D) plane varies with respect to its horizontal position is governed by the first order ordinary differential equation given by y(xy" - 4) dx + 4edy = 0 It is required to solve the explicit relationship y = f(x) between the two spatial coordinates at any particular time. Transform the given differential equation into the standard form of a Bermoulli differential equation y'+ P(x) y = Q(x) y". Reduce the Bernoulli differential equation into a First Order Linear Differential Equation (FOLDE) z' + P,(x) z = Q, (x) by replacing the dependent variable y with a new variable z = y". Solve for the Integrating Factor 1(x) of the resulting reduced first order linear differential equation. Substituting the expression for z, setup the solution of the Bernouli differential equation as