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* – 1) dx + 4e-*dy = 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 Bernoulli 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!-n. 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 Bernoulli differential equation as z- I(x) = | (1(x) · Q-(x)) dx